Answer: 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.
