review the graph. which function represents the graph? o y = -3cos(x) o y = -3sin(x) o y = 3cos(x) o y =…

Explanation:

Step1: Check the y - intercept

When (x = 0), for (y = A\sin(x)), (y=A\sin(0)=0), and for (y = A\cos(x)), (y = A\cos(0)=A). The graph passes through the origin ((0,0)), so the function is of the form (y = A\sin(x)), eliminating the cosine - based functions (y=-3\cos(x)) and (y = 3\cos(x)).

Step2: Check the amplitude and sign

The amplitude of the function (y = A\sin(x)) is (|A|). The maximum value of the graph is 3 and the minimum is - 3, so (|A| = 3), i.e., (A=\pm3). As (x) increases from (0) to (\frac{\pi}{2}), the function value increases. For (y = A\sin(x)), when (A>0), the function (y=\sin(x)) is increasing on the interval ((0,\frac{\pi}{2})). So (A = 3) and the function is (y = 3\sin(x)).

Answer:

(y = 3\sin(x))