Bài tập đường tiệm cận của đồ thị hàm số – Diệp Tuân

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Chào các bạn học sinh và quý thầy cô, hôm nay LogaVN gửi tới bạn đọc tài liệu "Bài tập đường tiệm cận của đồ thị hàm số – Diệp Tuân". Hi vọng sẽ giúp ích cho các bạn học tập và giảng dạy.

Tài liệu gồm 55 trang, được biên soạn bởi thầy giáo Diệp Tuân, phân dạng và tuyển chọn các bài tập tự luận & trắc nghiệm chuyên đề đường tiệm cận của đồ thị hàm số, giúp học sinh tự rèn luyện khi học chương trình Giải tích 12 chương 1: Ứng dụng đạo hàm để khảo sát và vẽ đồ thị hàm số.

A. LÍ THUYẾT
1. Đường tiệm cận đứng.
2. Đường tiệm cận ngang.
3. Đường tiệm cận xiên.
B. PHÂN DẠNG VÀ BÀI TẬP MINH HỌA
Dạng 1. Tìm các đường tiệm cận của đồ thị hàm số.
+ Tìm tiệm cận ngang, tiệm cận đứng của đồ thị hàm số.
+ Tìm tiệm cận xiên của đồ thị hàm số.
Dạng 2. Tìm tham số m để đồ thị hàm số có tiệm cận.
+ Đối với hàm số phân thức hữu tỉ.
+ Đối với hàm số y = √(ax^2 + bx + c) (với a khác 0).
Dạng 3. Các bài toán liên quan đến tiệm cận.
+ Xác định các đường tiệm cận.
+ Dựa vào các giả thiết: khoảng cách, góc, diện tích … thiết lập phương trình, hệ phương trình để tìm ẩn cần tìm.

Trung Tâm Luyện Thi Đại Học Amsterdam Chương I-Bài 4.Tiệm Cận của đồ thị hàm số 2 76 Lớp Toán Thầy-Diệp Tuân Tel: 0935.660.880 A. LÍ THUYẾT I. ĐƯỜNG TIỆM CẬN ĐỨNG. 1. Định nghĩa: Đường thẳng xx  được gọi là đường tiệm cận đứng (hay tiệm cận đứng) của đồ thị hàm số ()  y f x nếu ít nhất một trong các điều kiện sau được thỏa mãn: lim ( ) ,      xx fx lim ( ) ,      xx fx lim ( ) ,      xx fx lim ( ) .      xx fx 2. Nhận xét: Để tìm tiệm cận đứng của đồ thị hàm số, ta cần tính giới hạn một bên của , x với x thường là điều kiện biên của hàm số (hay tại x thì hàm số không xác định). Kỹ năng sử dụng máy tính (tham khảo):  Tính lim ( )   xx fx thì nhập () fx và CALC 9 10 .   xx  Tính lim ( )   xx fx thì nhập () fx và CALC 9 10 .   xx 2. ĐƯỢNG TIỆM CẬN NGANG. 1. Định nghĩa: Cho hàm số ()  y f x xác định trên một khoảng vô hạn (là khoảng ( ; ), ( ; )     ab … Đường thẳng 0 yy  là đường tiệm cận ngang (hay tiệm cận ngang) của đồ thị hàm số ()  y f x nếu ít nhất một trong các điều kiện sau được thỏa mãn: 00 . lim ( ) , lim ( ) xx f x y f x y        2. Nhận xét: Để tìm tiệm cận ngang của đồ thị hàm số ta cần tính giới hạn của hàm số tại vô cực. Tìm giới hạn ở vô cực của hàm () ; ()  Px y Qx với ( ), ( ) P x Q x là các đa thức không căn:  Bậc của () Px nhỏ hơn bậc của ()  Qx lim 0     x y Tiệm cận ngang : 0.  Ox y  Bậc của () Px bằng bậc của ()  Qx lim     x y HÖ sè bËc cao cña ( ) HÖ sè bËc cao cña ( ) x P x x Q x .   Suy ra tiệm cận ngang .   y  Bậc của () Px lớn hơn bậc của ()  Qx lim        x y Không có tiệm cận ngang. Kỹ năng sử dụng máy tính (tham khảo):  Tính lim ( )    x fx thì nhập () fx và CALC 10 10 .  x  Tính lim ( )    x fx thì nhập () fx và CALC 10 10 .  x 3. Ví dụ minh họa: Ví dụ 1. Tìm tiệm cận của hàm số: 1). 21 1    x y x . 2). 24 1    x y x . 3). 1 21 2     yx x . 4). 2 1   x y x . Lời giải. §B À I 4. TI ỆM C ẬN C ỦA Đ Ồ TH Ị HÀM S Ố Trung Tâm Luyện Thi Đại Học Amsterdam Chương I-Bài 4.Tiệm Cận của đồ thị hàm số 2 77 Lớp Toán Thầy-Diệp Tuân Tel: 0935.660.880 .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... 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III. ĐƯỜNG TIỆM CẬN XIÊN 1. Định nghĩa: Đường thẳng b, 0 y ax a    ,được gọi là đường tiệm cận xiên của đồ thị hàm số    y f x nếu ít nhất một trong các điều kiện sau được thỏa mãn:       lim 0          x f x f x ax b hoặc       lim 0          x f x f x ax b Trong đó     lim , lim            xx fx a b f x ax x hoặc     lim , lim            xx fx a b f x ax x . 2. Ví dụ minh họa: Ví dụ 2. Tìm tiệm cận của hàm số: 2 1   x y x Lời giải .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... Trung Tâm Luyện Thi Đại Học Amsterdam Chương I-Bài 4.Tiệm Cận của đồ thị hàm số 2 78 Lớp Toán Thầy-Diệp Tuân Tel: 0935.660.880 .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... B. PHÂN DẠNG VÀ BÀI TẬP MINH HỌA . Dạng 1. Tìm các đường tiệm cận của đồ thị hàm số. 1. Phương pháp. a). Tìm tiệm cận ngang, tiệm cận đứng của đồ thị hàm số. Đối với hàm phân thức:   () ()  Px fx Qx trong đó     , P x Q x là hai đa thức của x ta thường dùng phương pháp sau để tìm các đường tiệm cận của đồ thị hàm số Tiệm cận đứng .  Nếu 0 0 ( ) 0 ( ) 0      Px Qx thì đường thẳng : 0  xx là tiệm cận đứng của đồ thị hàm số Tiệm cận ngang  Nếu bậc của   Px bé hơn bậc của   Qx thì đồ thị của hàm số có tiệm cận ngang là trục hoành độ  Nếu bậc của   Px bằng bậc của   Qx thì đồ thị hàm có tiệm cận ngang là đường thẳng :  A y B trong đó , AB lần lượt là hệ số của số hạng có số mũ lớn nhất của   Px và   Qx .  Nếu bậc của   Px lớn hơn bậc của   Qx thì đồ thị của hàm số không có tiệm cận ngang b). Tìm tiệm cận xiên của đồ thị hàm số.  Nếu bậc của   Px bé hơn hay bằng bậc của   Qx hoặc lớn hơn bậc của   Qx từ hai bậc trở lên thì đồ thị hàm số không có tiệm cận xiên  Nếu bậc của   Px lớn hơn bậc của   Qx một bậc và   Px không chia hết cho   Px thì đồ thị hàm có tiệm cận xiên và ta tìm tiệm cận xiên bằng cách chia   Px cho   Qx và viết   () ab ()    Rx f x x Qx , trong đó ( ) ( ) lim 0 , lim 0 ( ) ( )        xx R x R x Q x Q x .  Suy ra đường thẳng : y ax b  là tiệm cận xiên của đồ thị hàm số. Chú ý: Xét hàm số   2 0     y ax bx c a .  Nếu 0  a đồ thị hàm số không có tiệm cận.  Nếu 0  a đồ thị hàm số có tiệm cận xiên 2     b y a x a khi    x và 2       b y a x a khi    x . Đồ thị hàm số   2 0       y mx n p ax bx c a có tiệm cận là đường thẳng : 2     b y mx n p a x a . 2. Bài tập minh họa. Bài tập 1. Tìm tiệm cận của hàm số: 1). 2 22    y x x 2). 2 1    y x x . Trung Tâm Luyện Thi Đại Học Amsterdam Chương I-Bài 4.Tiệm Cận của đồ thị hàm số 2 79 Lớp Toán Thầy-Diệp Tuân Tel: 0935.660.880 Lời giải. .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... 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Câu hỏi trắc nghiệm. Mức độ 1. Thông Hiểu Câu 1. Tìm phương trình đường tiệm cận ngang của đồ thị hàm số 3 32    x y x . A. 1 3  x . B. 2 3  x . C. 2 3  y . D. 1 3  y . 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Câu 2. Tiệm cận ngang của đồ thị hàm số 5 1   y x là đường thẳng có phương trình ? A. 5  y . B. 0  x . C. 1  x . D. 0  y . Trung Tâm Luyện Thi Đại Học Amsterdam Chương I-Bài 4.Tiệm Cận của đồ thị hàm số 2 80 Lớp Toán Thầy-Diệp Tuân Tel: 0935.660.880 Lời giải .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... Câu 3. Cho hàm số 21 2    x y x có đồ thị   C . Tìm tọa độ giao điểm I của hai đường tiệm cận của đồ thị   C . A.   2;2  I . B.   2;2 I . C.   2; 2  I . D.   2; 2  I . Lời giải .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... Câu 4. Tiệm cận đứng của đồ thị hàm số 3 2 32 32    xx y xx là đường thẳng : A. 2  x . B. Không có tiệm cận đứng. C. 1  x ; 2  x . D. 1  x . 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Câu 5. Đồ thị của hàm số nào trong các hàm số dưới đây có tiệm cận đứng? A. 2 1 . 1   y x B. 2 .  y x C. 2 1 . 2   y xx D. 4 3 . 1   y x Lời giải .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... Câu 6. Đồ thị của hàm số nào dưới đây có tiệm cận đứng? A. 2 32 1    xx y x . B. 2 2 1   x y x . C. 2 1  yx . D. 1   x y x . Lời giải .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... Trung Tâm Luyện Thi Đại Học Amsterdam Chương I-Bài 4.Tiệm Cận của đồ thị hàm số 2 81 Lớp Toán Thầy-Diệp Tuân Tel: 0935.660.880 .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... Câu 7. Đồ thị hàm số nào dưới đây có ba đường tiệm cận? A. 12 1    x y x . B. 2 1 4   y x . C. 3 51    x y x . D. 2 9   x y xx . 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Câu 8. Đồ thị hàm số 1 12    x y x có tiệm cận đứng là: A. 1 2  y . B. 1 2  x . C. 1 2  y . D. 1 2  x . 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Câu 9. Tìm số tiệm cận đứng của đồ thị hàm số 2 2 32 4    xx y x . A. 1. B. 2 . C. 3 . D. 4 Lời giải .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... Trung Tâm Luyện Thi Đại Học Amsterdam Chương I-Bài 4.Tiệm Cận của đồ thị hàm số 2 82 Lớp Toán Thầy-Diệp Tuân Tel: 0935.660.880 .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... Câu 10. Cho hàm số 2 2   x y x có đồ thị là đường cong   C . Khẳng định nào sau đây đúng? A.   C có hai tiệm cận đứng và một tiệm cận ngang. B.   C có hai tiệm cận đứng và hai tiệm cận ngang. C.   C có một tiệm cận đứng và một tiệm cận ngang. D.   C có hai tiệm cận đứng và không có tiệm cận ngang. Lời giải .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... Câu 11. Đồ thị của hàm số nào dưới đây có đường tiệm cận ngang? A. 42 22    y x x . B. 32 31    y x x . C. 2 41 2    x y x . D. 2 1 1    x y x . Lời giải .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... Câu 12. Đồ thị hàm số nào sau đây không có tiệm cận ngang? A. 2 1    x y x . B. 2 2 1    x y x . C. 2 1   x y x . D. 2 1    y x x Lời giải .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... Trung Tâm Luyện Thi Đại Học Amsterdam Chương I-Bài 4.Tiệm Cận của đồ thị hàm số 2 83 Lớp Toán Thầy-Diệp Tuân Tel: 0935.660.880 .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... Câu 13. Tìm số tiệm cận đứng của đồ thị hàm số 2 2 34 16    xx y x . A. 1. B. 2 . C. 0 . D. 3 . Lời giải .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... Câu 14. Tìm số tiệm cận của đồ thị hàm số 2 2 76 1    xx y x . A. 1. B. 2 . C. 3 . D. 0 . Lời giải .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... Câu 15. Cho hàm số    y f x có   lim 2     x fx và   lim 2     x fx . Khẳng định nào sau đây đúng? A. Đồ thị hàm số đã cho có đúng một tiệm cận ngang. B. Đồ thị hàm số đã cho không có tiệm cận ngang. C. Đồ thị hàm số đã cho có hai tiệm cận ngang là hai đường thẳng 2  x và 2  x . D. Đồ thị hàm số đã cho có tiệm cận ngang là hai đường thẳng 2  y và 2  y . Lời giải .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... Trung Tâm Luyện Thi Đại Học Amsterdam Chương I-Bài 4.Tiệm Cận của đồ thị hàm số 2 84 Lớp Toán Thầy-Diệp Tuân Tel: 0935.660.880 Câu 16. Cho hàm số    y f x có đồ thị là đường cong   C và các giới hạn   2 lim 1    x fx ;   2 lim 1    x fx ;   lim 2     x fx ;   lim 2     x fx . Hỏi mệnh đề nào sau đây đúng? A. Đường thẳng 2  y là tiệm cận ngang của   C . B. Đường thẳng 1  y là tiệm cận ngang của   C . C. Đường thẳng 2  x là tiệm cận ngang của   C . D. Đường thẳng 2  x là tiệm cận đứng của   C . Lời giải .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... Câu 17. Cho hàm số    y f x xác định trên   \0 , liên tục trên mỗi khoảng xác định và có bảng biến thiên như sau Chọn khẳng định đúng A. Đồ thị hàm số có đúng một tiệm cận ngang. B. Đồ thị hàm số có hai tiệm cận ngang. C. Đồ thị hàm số có đúng một tiệm cận đứng. D. Đồ thị hàm số không có tiệm đứng và tiệm cận ngang. Lời giải .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... Câu 18. Số đường tiệm cận của đồ thị hàm số 2 1   x y x A. 0 . B. 1. C. 2 . D. 3 . Lời giải .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... Câu 19. Cho hàm số 2 53 41    x y x . Số đường tiệm cận của đồ thị hàm số là A. 3 . B. 4 . C. 1. D. 2 . Trung Tâm Luyện Thi Đại Học Amsterdam Chương I-Bài 4.Tiệm Cận của đồ thị hàm số 2 85 Lớp Toán Thầy-Diệp Tuân Tel: 0935.660.880 Lời giải .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... Câu 20. Số tiệm cận ngang của đồ thị hàm số 2 2 1 4 4     y x x là A. 2 . B. 1. C. 0 . D. 3 . Lời giải .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... Mức độ 2. Thông Hiểu Câu 21. Đồ thị hàm số 2 2 6 34    x y xx có tất cả bao nhiêu đường tiệm cận. A. 2 . B. 3 . C. 0 . D. 1. Lời giải .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... Câu 22. Số tiệm cận đứng của đồ thị hàm số 2 93    x y xx là A. 3 . B. 2 . C. 0 . D. 1. Lời giải .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... Trung Tâm Luyện Thi Đại Học Amsterdam Chương I-Bài 4.Tiệm Cận của đồ thị hàm số 2 86 Lớp Toán Thầy-Diệp Tuân Tel: 0935.660.880 .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... Câu 23. Số tiệm cận đứng của đồ thị hàm số 2 42    y x xx là A. 3 . B. 0 . C. 2 . D. 1. Lời giải .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... Câu 24. Số tiệm cận đứng của đồ thị hàm số 2 25 5    x y xx là A. 2 . B. 0 . C. 1. D. 3 . Lời giải .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... Câu 25. Số tiệm cận đứng của đồ thị hàm số 2 16 4    x y xx là A. 0 . B. 3 . C. 2 . D. 1. Lời giải .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... Trung Tâm Luyện Thi Đại Học Amsterdam Chương I-Bài 4.Tiệm Cận của đồ thị hàm số 2 87 Lớp Toán Thầy-Diệp Tuân Tel: 0935.660.880 .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... Câu 26. Đồ thị hàm số 2 2 9    x y x có bao nhiêu đường tiệm cận? A. 2. B. 3. C. 0. D. 1. Lời giải .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... Câu 27. Số đường tiệm cận của đồ thị hàm số 2 2 1    xx y x là: A. 1. B. 2 . C. 0 . D. 3 . Lời giải .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... Câu 28. Số đường tiệm cận của đồ thị hàm số 2 1   x y x là: A. 1. B. 2 . C. 4 . D. 3 Lời giải. .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... Câu 29. Cho hàm số 1 2    x y x . Các đường tiệm cận đứng và tiệm cận ngang của đồ thị hàm số đã cho có phương trình lần lượt là: A. 2, 1  xy . B. 4, 1  xy . C. 1 1, 2    xy . D. 2, 1  xy . Lời giải .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... Trung Tâm Luyện Thi Đại Học Amsterdam Chương I-Bài 4.Tiệm Cận của đồ thị hàm số 2 88 Lớp Toán Thầy-Diệp Tuân Tel: 0935.660.880 .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... Câu 30. Tổng số đường tiệm cận đứng và tiệm cận ngang của đồ thị hàm số 2 1    xx y x bằng A. 2. B. 3. C. 4. D. 1. Lời giải .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... Câu 31. Đồ thị hàm số 2 1   xx y x có bao nhiêu tiệm cận? A. 0 . B. 3 . C. 1. D. 2 . Lời giải .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... Câu 32. Số đường tiệm cận của đồ thị hàm số   2 2018 2018    x y xx là A. 2 . B. 0 . C. 1. D. 3 . Lời giải Trung Tâm Luyện Thi Đại Học Amsterdam Chương I-Bài 4.Tiệm Cận của đồ thị hàm số 2 89 Lớp Toán Thầy-Diệp Tuân Tel: 0935.660.880 .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... Câu 33. Đồ thị hàm số 2 11 45    x y xx có tổng số bao nhiêu đường tiệm cận ngang và đứng? A. 1. B. 2 . C. 4 . D. 3 . Lời giải .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... Câu 34. Tìm số tiệm cận của đồ thị hàm số 1 1    x y x . A. 0 . B. 1. C. 2 . D. 3 . Lời giải .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... Trung Tâm Luyện Thi Đại Học Amsterdam Chương I-Bài 4.Tiệm Cận của đồ thị hàm số 2 9 0 Lớp Toán Thầy-Diệp Tuân Tel: 0935.660.880 Câu 35. Đồ thị hàm số   22 1 43     fx x x x x có bao nhiêu đường tiệm cận ngang ? A. 3 . B. 1. C. 4 . D. 2 . Lời giải .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... Câu 36. Đồ thị hàm số 2 51 21    xx y xx có bao nhiêu đường tiệm cận đứng và đường tiệm cận ngang? A. 3 . B. 1. C. 4 . D. 2 . Lời giải .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... Câu 37. Số đường tiệm cận đứng của đồ thị hàm số   2 3 3 2 sin 4    x x x y xx là A. 3 . B. 1. C. 2 . D. 4 . Lời giải .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... Trung Tâm Luyện Thi Đại Học Amsterdam Chương I-Bài 4.Tiệm Cận của đồ thị hàm số 2 9 1 Lớp Toán Thầy-Diệp Tuân Tel: 0935.660.880 .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... Câu 38. Tìm tất cả các đường tiệm cận đứng của đồ thị hàm số 2 51 4    x y xx . A. 4  x . B. Đồ thị hàm số không có tiệm cận đứng. C. 0  x . D. 0  x , 4  x . Lời giải .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... Câu 39. Số đường tiệm cận đứng và tiệm cận ngang của đồ thị hàm số 2 2 4 2 5 2    x y xx là A. 2 . B. 1. C. 3 . D. 4 . Lời giải .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... Câu 40. Đồ thị hàm số 2 2 4 56    x y xx có tất cả bao nhiêu đường tiệm cận đứng và tiệm cận ngang A. 1. B. 3 . C. 4 . D. 2 . Lời giải Trung Tâm Luyện Thi Đại Học Amsterdam Chương I-Bài 4.Tiệm Cận của đồ thị hàm số 2 9 2 Lớp Toán Thầy-Diệp Tuân Tel: 0935.660.880 .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... 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Câu 41. Số đường tiệm cận của đồ thị hàm số   22 1 2     y f x x x x x . A. 2 . B. 3 . C. 4 . D. 1. Lời giải .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... 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Câu 42. Đồ thị hàm số 11   x y x có bao nhiêu đường tiệm cận đứng và đường tiệm cận ngang. A. 2 . B. 0 . C. 3 . D. 1. Lời giải .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... Trung Tâm Luyện Thi Đại Học Amsterdam Chương I-Bài 4.Tiệm Cận của đồ thị hàm số 2 9 3 Lớp Toán Thầy-Diệp Tuân Tel: 0935.660.880 .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... Câu 43. Cho hàm số 3 2018 2    x y x   1 . Mệnh đề nào dưới đây là đúng? A. Đồ thị hàm số   1 có hai tiệm cận ngang 3  y , 3  y và không có tiệm cận đứng. B. Đồ thị hàm số   1 có đúng tiệm cận ngang 3  y và không có tiệm cận đứng. C. Đồ thị hàm số   1 không có hai tiệm cận ngang và có đúng một tiệm cận đứng 2  x . D. Đồ thị hàm số   1 có hai tiệm cận ngang 3  y , 3  y và có hai tiệm cận đứng 2  x , 2  x . Lời giải .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... Câu 44. Cho hàm số    y f x có bảng biến thiên như sau: Mệnh đề nào dưới đây đúng? A. Đồ thị hàm số có tiệm cận đứng là 1  x và tiệm cận ngang là 2  y . B. Đồ thị hàm số không có đường tiệm cận. C. Đồ thị hàm số chỉ có một đường tiệm cận. D. Đồ thị hàm số có tiệm cận ngang là đường thẳng 1  x và tiệm cận đứng là 2  y . Lời giải .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... Câu 45. Biết đồ thị hàm số    y f x có một tiệm cận ngang là 3  y . Khi đó đồ thị hàm số   24  y f x có một tiệm cận ngang là A. 3  y . B. 2  y . C. 1  y . D. 4  y . Lời giải .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... Trung Tâm Luyện Thi Đại Học Amsterdam Chương I-Bài 4.Tiệm Cận của đồ thị hàm số 2 9 4 Lớp Toán Thầy-Diệp Tuân Tel: 0935.660.880 .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... Câu 46. Cho hàm số    y f x có bảng biến thiên như hình dưới. Hỏi đồ thị hàm số    y f x có bao nhiêu đường tiệm cận: A. 3 . B. 4 . C. 2 . D. 1. Lời giải .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... Câu 47. Cho hàm số    y f x liên tục trên   \1 và có bảng biến thiên như sau:. Đồ thị hàm số   1 25   y fx có bao nhiêu đường tiệm cận đứng? A. 0 . B. 4 . C. 2 . D. 1. Lời giải .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... Mức độ 3. Vận dụng Câu 48. Đồ thị hàm số 2 5 1 1 2      xx y xx có tất cả bao nhiêu đường tiệm cận? A. 3 . B. 0 . C. 1. D. 2 . Lời giải .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... Trung Tâm Luyện Thi Đại Học Amsterdam Chương I-Bài 4.Tiệm Cận của đồ thị hàm số 2 9 5 Lớp Toán Thầy-Diệp Tuân Tel: 0935.660.880 .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... Câu 49. Tìm số đường tiệm cận của đồ thị hàm số 2 2    x y x . A. 1. B. 0 . C. 2 . D. 3 . Lời giải .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... Câu 50. Số đường tiệm cận đứng của đồ thị hàm số 22 2 4 1 3 2      xx y xx là A. 2 . B. 3 . C. 0 . D. 1. 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Câu 51. Hàm số    y f x xác định trên   \ 1;1  , có đạo hàm trên   \ 1;1  và có bảng biến thiên như sau Đồ thị hàm số   1 1   y fx có bao nhiêu tiệm cận (tiệm cận đứng và tiệm cận ngang)? A. 2 . B. 3 . C. 4 . D. 5 . Trung Tâm Luyện Thi Đại Học Amsterdam Chương I-Bài 4.Tiệm Cận của đồ thị hàm số 2 9 6 Lớp Toán Thầy-Diệp Tuân Tel: 0935.660.880 Lời giải .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... Câu 52. Cho hàm số    y f x liên tục trên   \1 và có bảng biến thiên như sau: Đồ thị hàm số   1 23   y fx có bao nhiêu đường tiệm cận đứng? A. 1. B. 2 . C. 0 . D. 2 . Lời giải .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... Câu 53. Hàm số    y f x có đạo hàm trên   \ 2;2  , có bảng biến thiên như sau: Gọi k , l lần lượt là số đường tiệm cận đứng và ngang của đồ thị hàm số   1 2018   y fx . Tính  kl . A. 2  kl . B. 3  kl . C. 4  kl . D. 5  kl . Lời giải .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... Trung Tâm Luyện Thi Đại Học Amsterdam Chương I-Bài 4.Tiệm Cận của đồ thị hàm số 2 9 7 Lớp Toán Thầy-Diệp Tuân Tel: 0935.660.880 .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... Mức độ 4. Vận dụng cao Câu 54. Cho hàm số bậc ba   y f x  có đồ thị là đường cong hình bên. Đồ thị hàm số     2 1 x gx fx    có tất cả bao nhiêu đường tiệm cận đứng A. 0. B. 1. C. 2. D. 3. Lời giải .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... Câu 55. Cho hàm trùng phương   y f x  có đồ thị là đường cong hình bên. Đồ thị hàm số       2018 1 x gx f x f x     có tất cả bao nhiêu đường tiệm cận ? A. 2. B. 3. C. 4. D. 9. 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Câu 56. Cho hàm trùng phương   y f x  có đồ thị là đường cong hình bên. Đồ thị hàm số     2018 2019 gx fx  có tất cả bao nhiêu đường tiệm cận ? A. 1. B. 2. C. 3. D. 4. Lời giải Trung Tâm Luyện Thi Đại Học Amsterdam Chương I-Bài 4.Tiệm Cận của đồ thị hàm số 2 9 8 Lớp Toán Thầy-Diệp Tuân Tel: 0935.660.880 .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... Câu 57. Cho hàm số bậc ba   y f x  có đồ thị là đường cong hình bên. Đồ thị hàm số       2 2 1 4 x gx f x f x    có tất cả bao nhiêu đường tiệm cận đứng ? A. 1. B. 2. C. 3. D. 4. 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Câu 58. Cho hàm số bậc ba   y f x  có đồ thị là đường cong hình bên. Đồ thị hàm số           2 2 11 2 xx gx f x f x    có tất cả bao nhiêu đường tiệm cận đứng ? A. 1. B. 2. C.3. D. 4. Lời giải .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... Trung Tâm Luyện Thi Đại Học Amsterdam Chương I-Bài 4.Tiệm Cận của đồ thị hàm số 2 9 9 Lớp Toán Thầy-Diệp Tuân Tel: 0935.660.880 .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... Câu 59. Cho hàm trùng phương   y f x  có đồ thị là đường cong hình bên. Đồ thị hàm số           2 2 11 2 x x x gx f x f x    có tất cả bao nhiêu đường tiệm cận đứng ? A. 1. B. 2. C. 3. D. 4. Lời giải .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... Câu 60. Cho hàm số bậc năm   y f x  liên tục trên và có đồ thị như hình vẽ. Đồ thị hàm số       3 3 49 xx gx f x f x    có bao nhiêu đường tiệm cận đứng ? A. 4. B. 5. C. 6. D. 7. 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Trung Tâm Luyện Thi Đại Học Amsterdam Chương I-Bài 4.Tiệm Cận của đồ thị hàm số 300 Lớp Toán Thầy-Diệp Tuân Tel: 0935.660.880 Câu 61. Cho hàm số bậc năm   y f x  liên tục trên và có đồ thị như hình vẽ. Đồ thị hàm số       2 2 x gx f x f x   có bao nhiêu đường tiệm cận đứng ? A. 1. B. 2. C. 3. D. 4. Lời giải .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... Câu 62. Cho hàm số bậc ba   y f x  có đồ thị là đường cong hình bên. Đồ thị hàm số         2 2 3 2 1 x x x gx x f x f x        có tất cả bao nhiêu đường tiệm cận đứng ? A. 2. B. 3. C. 4. D. 5. Lời giải .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... 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Câu 63. Cho hàm số bậc ba   y f x  có đồ thị là đường cong hình bên. Đồ thị hàm số         22 2 43 2 x x x x gx x f x f x        có tất cả bao nhiêu đường tiệm cận đứng ? A. 2. B. 3. C. 4. D. 5. Lời giải Trung Tâm Luyện Thi Đại Học Amsterdam Chương I-Bài 4.Tiệm Cận của đồ thị hàm số 30 1 Lớp Toán Thầy-Diệp Tuân Tel: 0935.660.880 .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... 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Câu 64. Cho hàm số bậc năm   y f x  liên tục trên và có đồ thị như hình vẽ. Đồ thị hàm số       3 21 49 xx gx f x f x    có bao nhiêu đường tiệm cận đứng ? A. 2. B. 3. C. 5. D. 7. Lời giải .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... Câu 65. Cho hàm bậc bốn   y f x  liên tục trên và có đồ thị như hình vẽ. Đồ thị hàm số       2 2 2 5 4 2 1 11 28 x x x x gx f x f x      có bao nhiêu đường tiệm cận đứng ? A. 3. B. 4. C. 5. D. 6. Lời giải .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... Trung Tâm Luyện Thi Đại Học Amsterdam Chương I-Bài 4.Tiệm Cận của đồ thị hàm số 302 Lớp Toán Thầy-Diệp Tuân Tel: 0935.660.880 .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... Câu 66. Cho hàm số bậc ba   y f x  có đồ thị như hình vẽ. Đồ thị hàm số           2 2 1 2 2 3 1 65 x x x x gx f x f x        có bao nhiêu đường tiệm cận đứng ? A. 1. B. 2. C. 3. D. 4. Lời giải .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... Câu 67. Cho hàm số bậc ba   y f x  có đồ thị như hình vẽ. Đồ thị hàm số       2 10 9 5 2 8 13 xx gx f x f x      có bao nhiêu đường tiệm cận đứng ? A. 1. B. 2. C. 3. D. 4. Lời giải .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... Trung Tâm Luyện Thi Đại Học Amsterdam Chương I-Bài 4.Tiệm Cận của đồ thị hàm số 303 Lớp Toán Thầy-Diệp Tuân Tel: 0935.660.880 .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... Câu 68. Cho hàm bậc ba   y f x  có đồ thị như hình. Đồ thị hàm số         2 2 1 4 3 fx gx x x x     có bao nhiêu đường tiệm cận đứng ? A. 1. B. 2. C. 3. D. 4. Lời giải .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... Câu 69. Cho hàm số   y f x  liên tục trên và có bảng biến thiên như hình bên. Tìm tất cả các số thực m để đồ thị hàm số     1 gx f x m   có ba đường tiệm cận đứng ? A. 5. m  B. 5. m  C. 5 4. m    D. 5 4. m    Lời giải .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... Câu 70. Cho hàm số y f x liên tục trên và có bảng biến thiên như hình bên. Hỏi đồ thị của hàm số đã cho có bao nhiêu đường tiệm cận (chỉ tính đường tiện đứng và đường tiệm cận ngang) ? A. 1. B. 2. C. 3. D. 4. Lời giải Trung Tâm Luyện Thi Đại Học Amsterdam Chương I-Bài 4.Tiệm Cận của đồ thị hàm số 304 Lớp Toán Thầy-Diệp Tuân Tel: 0935.660.880 .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... Câu 71. Hàm số   y f x  xác định và có đạo hàm trên   \ 1;1 ,  có bảng biến thiên như hình bên. Gọi , kl lần lượt là số đường tiệm cận đứng và tiệm cận ngang của đồ thị hàm số     1 1 gx fx   . Tính . kl  A. 2. kl  B. 3. kl  C. 4. kl  D. 5. kl  Lời giải .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... Câu 72. Cho hàm số   y f x  liên tục trên và có bảng biến thiên như hình vẽ. Đồ thị hàm số     2 1 1 gx fx   có bao nhiêu đường tiệm cận đứng ? A. 0. B. 1. C. 2. D. 3. Lời giải .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... Câu 73. Cho hàm số bậc ba   y f x  có bảng biến thiên như hình vẽ. Đồ thị hàm số     2 2 2 4 xx gx fx    có bao nhiêu đường tiệm cận đứng ? A. 1. B. 2. C. 3. D. 4. Lời giải .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... Trung Tâm Luyện Thi Đại Học Amsterdam Chương I-Bài 4.Tiệm Cận của đồ thị hàm số 305 Lớp Toán Thầy-Diệp Tuân Tel: 0935.660.880 .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... Câu 74. Cho hàm số   y f x  liên tục trên và có bảng biến thiên như hình vẽ. Đồ thị hàm số     1 32 gx fx   có bao nhiêu tiệm cận đứng ? A. 0. B. 1. C. 2. D. 3. Lời giải .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... Câu 75. Cho hàm số   y f x  liên tục trên và có bảng biến thiên như hình vẽ. Đồ thị hàm số     1 34 gx fx   có bao nhiêu tiệm cận đứng ? A. 0. B. 1. C. 2. D. 3. Lời giải .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... Câu 76. Cho hàm số   y f x  liên tục trên và có bảng biến thiên như hình vẽ. Đồ thị hàm số     2 2 1 log 4 gx fx   có bao nhiêu tiệm cận đứng ? A. 1. B. 2. C. 3. D. 4. Lời giải .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... Trung Tâm Luyện Thi Đại Học Amsterdam Chương I-Bài 4.Tiệm Cận của đồ thị hàm số 30 6 Lớp Toán Thầy-Diệp Tuân Tel: 0935.660.880 .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... Câu 77. Cho hàm số   y f x  liên tục trên và có bảng biến thiên như hình vẽ. Đồ thị hàm số     2 2018 fx gx ee   có bao nhiêu tiệm cận đứng ? A. 3. B. 4. C. 5. D. 6. Lời giải .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... Câu 78. Cho hàm số bậc ba   y f x  có bảng biến thiên như hình. Đồ thị hàm số     2 7 3 4 5 1 xx gx fx      có bao nhiêu đường tiệm cận đứng ? A. 1. B. 2. C. 3. D. 4. Lời giải .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... Trung Tâm Luyện Thi Đại Học Amsterdam Chương I-Bài 4.Tiệm Cận của đồ thị hàm số 30 7 Lớp Toán Thầy-Diệp Tuân Tel: 0935.660.880 Dạng 2. Tìm tham số m để đồ thị hàm số có tiệm cận. 1. Phương pháp  Đối với hàm phân thức :   () ()  Px fx Qx trong đó là hai đa thức của x ta thường dùng phương pháp sau để tìm các đường tiệm cận của đồ thị hàm số Tiệm cận đứng.  Nếu 0 0 ( ) 0 ( ) 0      Px Qx thì đường thẳng : 0  xx là tiệm cận đứng của đồ thị hàm số.  Đối với hàm số   2 0     y ax bx c a .  Nếu 0  a đồ thị hàm số không có tiệm cận.  Nếu 0  a đồ thị hàm số có tiệm cận ngang khi    x 2. Bài tập minh họa. Bài tập 2.Tùy theo giá trị của tham số  m , tìm tiệm cận của đồ thị hàm số sau: 3 1 1    x y mx . Lời giải. .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... Bài tập 3. Tìm các giá trị của tham số m để đồ thị của hàm số 2 1 x y xm    có hai tiệm cận đứng Lời giải .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... .........................................................................................................................................................................................................     , P x Q x Trung Tâm Luyện Thi Đại Học Amsterdam Chương I-Bài 4. Tiệm Cận của đồ thị hàm số 30 8 Lớp Toán Thầy-Diệp Tuân Tel: 0935.660.880 3. Câu hỏi trắc nghiệm Mức độ 2. Thông Hiểu Câu 79. Tìm tất cả các giá trị của tham số m để đồ thị hàm số 24    x y xm có tiệm cận đứng. A. 2  m . B. 2  m . C. 2  m . D. 2  m . Lời giải .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... Câu 80. Cho hàm số    y f x có   lim 3    x fx và   lim 3    x fx . Khẳng định nào sau đây đúng? A. Đồ thị hàm số có đúng một tiệm cận ngang. B. Đồ thị hàm số có hai tiệm cận ngang là các đường thẳng 3  y ; 3  y . C. Đồ thị hàm số không có tiệm cận ngang. D. Đồ thị hàm số có hai tiệm cận ngang là các đường thẳng 3  x ; 3  x . Lời giải .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... Câu 81. Tìm tất cả các giá trị của tham số m để đồ thị hàm số 2 2 1    x y x mx có hai đường tiệm cận đứng. A.     5 ; 2 2; \ 2         m . B.     ; 2 2;        m . C.     ; 2 2;        m . D. 5 2  m . Lời giải .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... Câu 82. Tìm tất cả các giá trị của tham số thực m để đồ thị hàm số 2 1    mx y x luôn có tiệm cận ngang. A. .  m . B. 2.    m C. 2.  m D. 1 . 2  m Lời giải .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... Trung Tâm Luyện Thi Đại Học Amsterdam Chương I-Bài 4. Tiệm Cận của đồ thị hàm số 30 9 Lớp Toán Thầy-Diệp Tuân Tel: 0935.660.880 .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... Câu 83. Biết đồ thị hàm số   2 2 2 x 1 x6        m n x m y x m n (m , n là tham số) nhận trục hoành và trục tung làm hai đường tiệm cận. Tính  mn A. 6 . B. 6  . C. 8 . D. 9 . Lời giải .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... Câu 84. Tìm tập hợp tất cả các giá trị của tham số m để đồ thị hàm số 22 1 2      x m x m y x có tiệm cận đứng. A.   \ 1; 3  . B. . C. 2 \ 1; 3     . D. 3 \ 1; 2     . Lời giải .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... Câu 85. Tìm tất cả giá trị thực của tham số m để đồ thị hàm số 2 2 1    x y x mx có đúng 3 đường tiệm cận. A. 2 5 . 2 2              m m m B. 2 2 . 5 2               m m m C. 2 . 2      m m D. 2 2.    m Lời giải .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... Trung Tâm Luyện Thi Đại Học Amsterdam Chương I-Bài 4. Tiệm Cận của đồ thị hàm số 310 Lớp Toán Thầy-Diệp Tuân Tel: 0935.660.880 .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... Câu 86. Cho hàm số 2 2 1    xm y xm . Tìm tất cả các giá trị thực của tham số m để đường tiệm cận đứng của đồ thị hàm số đi qua điểm   3;1 M A. 1  m . B. 3  m . C. 3  m . D. 2  m . Lời giải .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... Câu 87. Cho hàm số 2 2    x y x mx m . Số giá trị của tham số thực m để đồ thị hàm số có đúng hai đường tiệm cận là A. 1. B. 2 . C. 3 . D. 4 . Lời giải .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... Câu 88. Cho hàm số 1    ax b y bx có đồ thị   C . Nếu   C có tiệm cận ngang là đường thẳng 2  y và tiệm cận đứng là đường thẳng 1 3  x thì các giá trị của a và b lần lượt là A. 1 2  và 1 6  . B. 3  và 6  . C. 1 6  và 1 2  . D. 6  và 3  . Lời giải .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... Trung Tâm Luyện Thi Đại Học Amsterdam Chương I-Bài 4. Tiệm Cận của đồ thị hàm số 311 Lớp Toán Thầy-Diệp Tuân Tel: 0935.660.880 .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... Câu 89. Tìm giá trị của m để đồ thị hàm số  12 1    mx y x có đường tiệm cận ngang đi qua điểm   3;1 A : A. 2  m . B. 0  m . C. 2  m . D. 4  m . Lời giải .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... Câu 90. Tìm tất cả giá trị thực của tham số m để đồ thị hàm số 2 2 1    x y x mx có đúng 3 đường tiệm cận. A. 2 2      m m . B. 22    m . C. 2 2 5 2               m m m . D. 2 5 2 2              m m m . Lời giải .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... Câu 91. Tìm tất cả các giá trị thực của tham số m sao cho đồ thị hàm số 2 23    x x m y xm không có tiệm cận đứng. A. 1  m . B. 0  m . C. 1  m . D. 1  m và 0  m . Lời giải .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... Trung Tâm Luyện Thi Đại Học Amsterdam Chương I-Bài 4. Tiệm Cận của đồ thị hàm số 312 Lớp Toán Thầy-Diệp Tuân Tel: 0935.660.880 .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... Câu 92. Có bao nhiêu giá trị m để đồ thị hàm số 2 2 1 32    mx y xx có đúng 2 đường tiệm cận ? A. 3 . B. 2 . C. 1. D. 4 . Lời giải .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... Câu 93. Tìm tập hợp tất cả các giá trị của tham số m để đồ thị hàm số 22 1 2      x m x m y x có tiệm cận đứng. A.   \ 1; 3  . B. . C. 2 \ 1; 3     . D. 3 \ 1; 2     . Lời giải .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... Câu 94. Tìm tất cả các giá trị của tham số thực m để đồ thị hàm số 2 1    mx y x luôn có tiệm cận ngang. A. .  m B. 2.    m C. 2.  m D. 1 . 2  m Lời giải .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... Trung Tâm Luyện Thi Đại Học Amsterdam Chương I-Bài 4. Tiệm Cận của đồ thị hàm số 313 Lớp Toán Thầy-Diệp Tuân Tel: 0935.660.880 .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... Câu 95. Đồ thị hàm số 2 21 21    mx x y x có tiệm cận đứng và tiệm cận xiên (hoặ c ngang) khi và chỉ khi A. 0  m . B. 4  m . C. 8  m . D. 8  m . Lời giải .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... Câu 96. Tìm tất cả các giá trị thực của tham số m để đồ thị hàm số   2 1 14    x y mx có hai tiệm cận đứng: A. 0.  m B. 0.  m C. 0 . 1      m m D. 1.  m Lời giải .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... Câu 97. Tìm tất cả các giá trị thực của tham số m để đồ thị hàm số 2 4 2 3    x y mx có một đường tiệm cận ngang. A. 0  m . B. 3  m . C. 0  m . D. 0  m . Lời giải .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... Câu 98. Biết rằng đồ thị của hàm số     3 2018 3      a x a y xb nhận trục hoành làm tiệm cận ngang và trục tung là tiệm cận đứng. Khi đó giá trị của  ab là A. 3 . B. 3  . C. 0 . D. 6 . Lời giải .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... Trung Tâm Luyện Thi Đại Học Amsterdam Chương I-Bài 4. Tiệm Cận của đồ thị hàm số 314 Lớp Toán Thầy-Diệp Tuân Tel: 0935.660.880 .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... Câu 99. Phương trình đường tiệm cận ngang của đồ thị hàm số 2 2 4 1      y x m x x (với m là tham số) là A. 41 . 4   m y B. 41 . 4   m y C. 21 . 2   m y D. 21 . 2   m y Lời giải .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... Câu 100. Có bao nhiêu giá trị của m để đồ thị hàm số  21 23 mx y x    có một tiệm cận ngang là 2.  y A. 1. B. 2 . C. 0 . D. Vô số. Lời giải .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... Mức độ 3. Vận Dụng Câu 101. Tìm tất cả các giá trị thực của tham số m sao cho đồ thị hàm số 22 1 1    x y m x m có bốn đường tiệm cận. A. 0  m . B. Với mọi giá trị của m . C. 1  m , 0  m và 15 2    m . D. 1  m hoặc 1  m . Trung Tâm Luyện Thi Đại Học Amsterdam Chương I-Bài 4. Tiệm Cận của đồ thị hàm số 315 Lớp Toán Thầy-Diệp Tuân Tel: 0935.660.880 Lời giải .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... Câu 102. Tìm tất cả các giá trị của tham số thực m sao cho đồ thị hàm số 32 1 31      x y x x m có đúng một tiệm cận đứng. A. 5 1      m m . B. 51     m . C. 5 1      m m . D. 4 0      m m . Lời giải .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... Câu 103. Tập hợp các giá trị của m để đồ thị của hàm số     22 21 2 1 4 4 1       x y mx x x m có đúng 1 đường tiệm cận là A.       ; 1 0 1;        . B.  . C.   0 . D.     ; 1 1;       . Lời giải .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... Trung Tâm Luyện Thi Đại Học Amsterdam Chương I-Bài 4. Tiệm Cận của đồ thị hàm số 316 Lớp Toán Thầy-Diệp Tuân Tel: 0935.660.880 .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... Câu 104. Cho hàm số 2 2 12 4 62    xx y x x m có đồ thị   m C . Tìm tập S tất cả các giá trị của tham số thực m để   m C có đúng hai tiệm cận đứng A.   8; 9  S . B. 9 4; 2      S . C. 9 4; 2     S . D.   0; 9  S . Lời giải .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... Câu 105. Tìm tất cả giá trị thực của tham số m để đồ thị hàm số 2 2 1    x y x mx có đúng 3 đường tiệm cận. A. 2 . 2      m m B. 2 2.    m C. 2 2 . 5 2               m m m D. 2 5 . 2 2              m m m Lời giải .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... Trung Tâm Luyện Thi Đại Học Amsterdam Chương I-Bài 4. Tiệm Cận của đồ thị hàm số 317 Lớp Toán Thầy-Diệp Tuân Tel: 0935.660.880 .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... Mức độ 4. Vận Dụng cao Câu 106. Tìm tất cả các giá trị của tham số m để đồ thị hàm số 2 1 2 2 1       x y x x m x có đúng bốn đường tiệm cận. A.     5;4 \ 4    m . B.   5;4  m . C.     5;4 \ 4    m . D.     5;4 \ 4    m Lời giải .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... Câu 107. Tìm tất cả các giá trị của tham số m sao cho đồ thị hàm số   22 1 1    mx x y xx có hai đường tiệm cận ngang. A. Không tồn tại m B. 0  m . C. 0  m . D. 0  m . Lời giải .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... Dạng 3. Các bài toán liên quan đến tiệm cận. 1. Phương pháp Bước 1. Xác định các đường tiệm cận. Bước 2. Dựa vào các giả thiết: khoảng cách, góc, diện tích…thiết lập phương trình, hệ phương trình để tìm ẩn cần tìm. Trung Tâm Luyện Thi Đại Học Amsterdam Chương I-Bài 4. Tiệm Cận của đồ thị hàm số 318 Lớp Toán Thầy-Diệp Tuân Tel: 0935.660.880 2. Bài tập minh họa. Bài tập 4. Cho hàm số 1 21 2     yx x có đồ thị là   C . Gọi M là một điểm bất kỳ thuộc   C , qua M vẽ hai đường thẳng lần lượt song song với hai đường tiệm cận của   C , hai đường thẳng này tạo với hai đường tiệm cận một hình bình hành, chứng minh hình bình hành này có diện tích không đổi. Lời giải. .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... Bài tập 5. Tìm  m để hàm số 1  y mx x có cực trị và khoảng cách từ điểm cực tiểu của hàm số đã cho đến đường tiệm cận xiên của nó bằng 2 17 . Lời giải. .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... Bài tập 6. Cho hàm số 2 3    x y x , có đồ thị là   C . Tìm tất cả các điểm M thuộc   C sao cho khoảng cách từ M đến tiệm cận đứng bằng 5 lần khoảng cách từ M đến tiệm cận ngang. Lời giải. Trung Tâm Luyện Thi Đại Học Amsterdam Chương I-Bài 4. Tiệm Cận của đồ thị hàm số 319 Lớp Toán Thầy-Diệp Tuân Tel: 0935.660.880 .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... Bài tập 7. Tìm trên đồ thị   2 : 3    x Cy x những điểm M sao cho khoảng cách từ điểm M đến đường tiệm cận đứng bằng 1 5 khoảng cách từ điểm M đến đường tiệm cận ngang. Lời giải. .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... Bài tập 8. Cho hàm số: 2    mx y xm có đồ thị là   m C . Cho   0;1 A và I là tâm đối xứng. Tìm m để trên   m C tồn tại điểm B sao cho tam giác ABI vuông cân tại A . Lời giải. .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... Trung Tâm Luyện Thi Đại Học Amsterdam Chương I-Bài 4. Tiệm Cận của đồ thị hàm số 320 Lớp Toán Thầy-Diệp Tuân Tel: 0935.660.880 .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... 3. Câu hỏi trắc nghiệm Mức độ 1. Nhận Biết Câu 108. Hàm số    y f x có bảng biến thiên dưới đây. Số tiệm cận của đồ thị hàm số    y f x là: A. 2 . B. 3 . C. 1. D. 4 . Lời giải .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... Câu 109. Cho hàm số    y f x liên tục trên và có bảng biến thiên như sau Mệnh đề nào dưới đây đúng? A. Đồ thị hàm số    y f x không có đường tiệm cận. B. Hàm số    y f x có điểm cực đại bằng 4 . C. Hàm số   y f x  đồng biến trên   5;2  . D. Hàm số    y f x có cực tiểu bằng 5  . Lời giải .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... Câu 110. Cho hàm số    y f x có bảng biển thiên sau Khẳng định nào sau đây là đúng? A. Đồ thị hàm số có tiệm cận đứng 1  x , tiệm cận ngang 1  y . B. Đồ thị hàm số có tiệm cận đứng 1  x , tiệm cận ngang 1  y . C. Đồ thị hàm số chỉ có một đường tiệm cận có phương trình 1  x . D. Đồ thị hàm số chỉ có một đường tiệm cận có phương trình 1  y . Lời giải .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... Trung Tâm Luyện Thi Đại Học Amsterdam Chương I-Bài 4. Tiệm Cận của đồ thị hàm số 32 1 Lớp Toán Thầy-Diệp Tuân Tel: 0935.660.880 .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... Câu 111. Cho hàm số    y f x có bảng biến thiên như hình vẽ. Khẳng định nào sau đây sai? A. Phương trình   50  fx có hai nghiệm thực. B. Đường thẳng 2  x là tiệm cận đứng của đồ thị hàm số. C. Hàm số đồng biến trên khoảng   ;1  . D.       3;10 max 10   x f x f . Lời giải .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... Câu 112. Cho hàm số ()  y f x có bảng biến thiên như sau 2 -3 x y' y -1 2 4 0 - + - 1 Chọn mệnh đề sai? A. Đồ thị hàm số có đường tiệm cận đứng 2  x . B. Hàm số có đúng 1 điểm cực trị. C. Hàm số đạt giá trị lớn nhất bằng 2 tại x bằng 4 . D. Hàm số đồng biến trên khoảng   2;3 . Lời giải .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... Trung Tâm Luyện Thi Đại Học Amsterdam Chương I-Bài 4. Tiệm Cận của đồ thị hàm số 322 Lớp Toán Thầy-Diệp Tuân Tel: 0935.660.880 Câu 113. Cho hàm số 3  m có bảng biến thiên như sau Đồ thị hàm số   fx có bao nhiêu tiệm cận đứng A.  xm B. 30    x C.   fx D.0. Lời giải .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... Mức độ 2. Thông Hiểu Câu 114. Gọi (H) là đồ thị hàm số 23 1    x y x . Điểm 00 ( ; ) M x y thuộc (H) có tổng khoảng cách đến hai đường tiệm cận là nhỏ nhất, với 0 0  x khi đó 00  xy bằng? A. 2  . B. 1  . C. 0 . D. 3 . Lời giải .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... Câu 115. Đường tiệm cận đứng và đường tiệm cận ngang của đồ thị hàm số 1 21    mx y mx cùng với hai trục tọa độ tạo thành một hình chữ nhật có diện tích bằng 3 . Tìm m . A. 1  m ; 3 2  m . B. 1  m ; 3 2  m . C. 1  m ; 3 2  m . D. 1  m ; 3  m . Lời giải .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... Trung Tâm Luyện Thi Đại Học Amsterdam Chương I-Bài 4. Tiệm Cận của đồ thị hàm số 323 Lớp Toán Thầy-Diệp Tuân Tel: 0935.660.880 .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... Câu 116. Tọa độ điểm M thuộc đồ thị hàm số 31 1    x y x cách đường tiệm cận đứng của đồ thị hàm số một khoảng bằng 1 là A.     0; 1 ; 2;7  . B.     1;0 ; 2;7  . C.     0;1 ; 2; 7  . D.     0; 1 ; 2;7  . Lời giải .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... Câu 117. Cho đồ thị hai hàm số   21 1    x fx x và   1 2    ax gx x với 1 2  a . Tìm tất cả các giá trị thực dương của a để các tiệm cận của hai đồ thị hàm số tạo thành một hình chữ nhật có diện tích là 4 . A. 1  a . B. 4  a . C. 3  a . D. 6. . Lời giải .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... Câu 118. Đường tiệm cận đứng và đường tiệm cận ngang của đồ thị hàm số 1 21    mx y mx cùng với hai trụ tọa độ tạo thành một hình chữ nhật có diện tích bằng 3 . Tìm m . A. 1  m ; 3 2  m . B. 1  m ; 3 2  m . C. 1  m ; 3 2  m . D. 1  m ; 3  m . Lời giải .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... Trung Tâm Luyện Thi Đại Học Amsterdam Chương I-Bài 4. Tiệm Cận của đồ thị hàm số 324 Lớp Toán Thầy-Diệp Tuân Tel: 0935.660.880 Câu 119. Gọi   H là đồ thị hàm số 23 1    x y x . Điểm 00 ( ; ) M x y thuộc   H có tổng khoảng cách đến hai đường tiệm cận là nhỏ nhất, với 0 0  x khi đó 00  xy bằng? A. 2  . B. 1  . C. 0 . D. 3 . Lời giải .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... Câu 120. Cho hàm số 2 43 23    xx y x   C . Gọi m là số tiệm cận của đồ thị hàm số   C và n là giá trị của hàm số   C tại 1  x thì tích . mn là: A. 6 5 . B. 14 5 . C. 3 5 . D. 2 15 . Lời giải .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... Câu 121. Biết rằng hai đường tiệm cận của đồ thị hàm số 21    x y xm (m là tham số thực) tạo với hai trục tọa độ một hình chữ nhật có diện tích bằng 2 . Giá trị của m bằng bao nhiêu? A. 1  m . B. 2  m . C. 2  m . D. 1  m . Lời giải .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... Mức độ. Vận dụng thấp Câu 122. Cho hàm số 2 2 1 49    ax x y x bx có đồ thị   C , trong đó a , b là các hằng số dương thỏa mãn .4  ab . Biết rằng   C có đường tiệm cận ngang  yc và có đúng 1 đường tiệm cận đứng. Tính tổng 3 24    T a b c . A. 11  T . B. 4  T . C. 7  T . D. 11  T . Trung Tâm Luyện Thi Đại Học Amsterdam Chương I-Bài 4. Tiệm Cận của đồ thị hàm số 325 Lớp Toán Thầy-Diệp Tuân Tel: 0935.660.880 Lời giải .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... Câu 123. Khoảng cách từ điểm   5;1  A đến đường tiệm cận đứng của đồ thị hàm số 2 2 1 2    x y xx A. 5 . B. 26 . C. 9 . D. 1. Lời giải .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... Câu 124. Cho đồ thị   C của hàm số 22 1    x y x . Tọa độ điểm M nằm trên   C sao cho tổng khoảng cách từ M đến hai tiệm cận của   C nhỏ nhất là A.   1;0  M hoặc   3;4 M . B.   1;0  M hoặc   0; 2  M . C.   2;6 M hoặc   3;4 M . D.   0; 2  M hoặc   2;6 M . Lời giải .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... Trung Tâm Luyện Thi Đại Học Amsterdam Chương I-Bài 4. Tiệm Cận của đồ thị hàm số 32 6 Lớp Toán Thầy-Diệp Tuân Tel: 0935.660.880 .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... Câu 125. Cho hàm số 2 1    x y x có đồ thị   C . Gọi d là khoảng cách từ giao điểm hai tiệm cận của đồ thị   C đến một tiếp tuyến của   C . Giá trị lớn nhất của d có thể đạt được là: A. 2 . B. 33 . C. 3 . D. 22 . Lời giải .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... Câu 126. Cho hàm số 22 2    x y x có đồ thị là   C , M là điểm thuộc   C sao cho tiếp tuyến của   C tại M cắt hai đường tiệm cận của   C tại hai điểm A , B thỏa mãn 25  AB . Gọi S là tổng các hoành độ của tất cả các điểm M thỏa mãn bài toán. Tìm giá trị của S . A. 6 . B. 5 . C. 8 . D. 7 . Lời giải .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... Câu 127. Cho hàm số 1 2    x y x , gọi d là tiếp tuyến với đồ thị hàm số tại điểm có hoành độ bằng 2  m . Biết đường thẳng d cắt tiệm cận đứng của đồ thị hàm số tại điểm   11 ; A x y và cắt tiệm cận ngang của đồ thị hàm số tại điểm   22 ; B x y . Gọi S là tập hợp các số m sao cho 21 5    xy . Tính tổng bình phương các phần tử của S . A. 0 . B. 4 . C. 10 . D. 9 . Trung Tâm Luyện Thi Đại Học Amsterdam Chương I-Bài 4. Tiệm Cận của đồ thị hàm số 32 7 Lớp Toán Thầy-Diệp Tuân Tel: 0935.660.880 Lời giải .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... Câu 128. Cho hàm số 2 2    x y x có đồ thị   C . Gọi I là giao điểm hai đường tiệm cận của   C . Tiếp tuyến của   C cắt hai đường tiệm cận của   C tại hai điểm A , B . Giá trị nhỏ nhất của chu vi đường tròn ngoại tiếp tam giác IAB bằng A. 42  . B. 8  . C. 2  . D. 4  . Lời giải .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... Câu 129. Cho hàm số 13 3    x y x có đồ thị   C . Điểm M nằm trên   C sao cho khoảng cách từ M đến tiệm cận đứng gấp hai lần khoảng cách từ M đến tiệm cận ngang của   C . Khoảng cách từ M đến tâm đối xứng của   C bằng A. 32 . B. 25 . C. 4 . D. 5 . Lời giải .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... Trung Tâm Luyện Thi Đại Học Amsterdam Chương I-Bài 4. Tiệm Cận của đồ thị hàm số 32 8 Lớp Toán Thầy-Diệp Tuân Tel: 0935.660.880 .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... Câu 130. Cho đồ thị   C của hàm số 22 1    x y x . Tọa độ điểm M nằm trên   C sao cho tổng khoảng cách từ M đến hai tiệm cận của   C nhỏ nhất là A.   1;0  M hoặc   3;4 M . B.   1;0  M hoặc   0; 2  M . C.   2;6 M hoặc   3;4 M . D.   0; 2  M hoặc   2;6 M . Lời giải .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... Mức độ 4. Vận dụng cao Câu 131. Tìm tọa độ điểm M có hoành độ dương thuộc đồ thị   C của hàm số 2 2 x y x    sao cho tổng khoảng cách từ M đến hai đường tiệm cận của đồ thị   C đạt giá trị nhỏ nhất. A.   1; 3 M  . B.   3;5 M . C.   0; 1 M  . D.   4;3 M Lời giải .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... Trung Tâm Luyện Thi Đại Học Amsterdam Chương I-Bài 4. Tiệm Cận của đồ thị hàm số 32 9 Lớp Toán Thầy-Diệp Tuân Tel: 0935.660.880 .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... Câu 132. Cho hàm số 21 1 x y x      C , gọi I là tâm đối xứng của đồ thị   C và   ; M a b là một điểm thuộc đồ thị. Tiếp tuyến của đồ thị   C tại điểm M cắt hai tiệm cận của đồ thị   C lần lượt tại hai điểm A và B . Để tam giác IAB có bán kính đường tròn nội tiếp lớn nhất thì tổng ab  gần nhất với số nào sau đây? A. 3  . B. 0 . C. 3 . D. 5 . Lời giải .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... 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Câu 133. Cho đường cong   23 : 1 x Cy x    và M là một điểm nằm trên   C . Giả sử 1 d , 2 d tương ứng là các khoảng cách từ M đến hai tiệm cận của   C , khi đó 12 . dd bằng: A. 3 . B. 4 . C. 5 . D. 6 . Lời giải .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... Trung Tâm Luyện Thi Đại Học Amsterdam Chương I-Bài 4. Tiệm Cận của đồ thị hàm số 330 Lớp Toán Thầy-Diệp Tuân Tel: 0935.660.880 .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... Câu 134. Cho hàm số 1 2 x y x    có đồ thị   C . Gọi I là giao điểm của hai tiệm cận của   C . Xét tam giác đều ABI có hai đỉnh A , B thuộc   C , đoạn thẳng AB có độ dài bằng A. 6 . B. 23 . C. 2 . D. 22 . Lời giải .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .......................................................................................................................................................................................................... ......................................................................................................................................................................................................... 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