We are given a graph with max=4, min=0, period=`(2pi)/3` (There are 3 repetitions from `-pi/2` to `(3pi)/2` ).
So `a=+-2,b=(2pi)/((2pi)/3)=3,k=2` where the function is `y=asin(b(x-h))+k` .
Since the function begins at the midline at x=0 but descends, we know that a=-2.
So the equation is y=-2sin(3x)+2.
The answer is (a)