Analysis and Approaches for IBDP Maths Ebook 2 | Page 79

Exercise 25
1. The function f is defined as f ( x) � Acosec
Bx � C , 0�x
� 6, A , B , C � . The
coordinates of the first local minimum and the first local maximum of the graph of f are
��
�
� ,3�
� 4 � and �3�
7�
� , �
� 4 3� respectively.
(a) Find the values of A , B and C .
(b) Write down the range of f .
[4]
[1]
2. The function f is defined as f ( x) � Asec( x � B)
� C , x � 0 , A , B , C � . The graph
��
�
of f passes through P � , �1�
� 6 � and Q ��
2
, 2 �
� �. It is given that P is the first local
� �
minimum.
(a) Find the values of A , B and C .
(b) Write down the range of f .
[4]
[1]
7
3. The function f is defined as f ( x) � Acot
Bx � C , 0�x
� 2, A , B , C � . The graph
of f passes through
�1 1�
� , �
�8 4� . The first two x -intercepts are 1 4 and 3 4 .
(a) Find the values of A , B and C .
(b) Write down the equations of the three asymptotes of f .
[4]
[2]
4. The function f is defined as f ( x) � Acosec
Bx � C , 0�x
� 4, A , B , C � . The
coordinates of the first local maximum and the second local minimum of the graph of f
are
�3 , 4
2 � �
� � �
� � and �5 , 4
2 � �
� � �
� � respectively.
(a) Find the values of A , B and C .
(b) Solve the equation f( x) �8� � .
[4]
[4]
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