9 . The graph of f is given by f ( t) � asin b( t �c)
� d , a � 0 , t � 0 .
When t � 2, there is a maximum value of 37 , at P . When t � 11, there is a minimum value of � 5 . The graph of f is strictly decreasing at 2 �t
� 11.
( a ) ( i ) Show that a � 21.
( ii ) Find the exact value of b .
( iii ) Find the value of d .
( iv ) Write down a possible value of c . [ 7 ]
The graph of f is then transformed to the graph of g by a horizontal stretch
� of scale factor 3 , followed by a translation of 17 � � �. Let P� be the image of P . � 8 �
( b ) Find the coordinates of P� .
The graph of g is then transformed to the graph of h by a translation of
[ 2 ] ��5� � �. �12
�
( c ) Give a full geometric description of the transformation that maps the graph of h to the graph of f .
[ 3 ]
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