Which of the following functions corresponds to the sinusoid shown?

4 sin 3x
-3 cos 4x
-4 cos 3x
3 sin 2x

the third option: -4cos(3x)

Justification:

1)  The amplitude of the function of the graph is [4 - (-4) ] / 2 = [4+4] / 2 = 8/2 = 4.

2) Therofore the coefficient that multiplies the trigonometric function is 4.

3) That leaves you the first and the third options:

4sin(3x) and - 4cos(3x).

4) The y intercept of the graph, f(0), is - 4.

Check f(0) for both 4 sin(3x) and 4 cos(3x)

4sin(0) = 0 => this is not the function

- 4cos(0) = -4 => this is the function and thw answer to the question.