-- The function is a sine or cosine that wiggles from 3 below to 3 above its average value. So the amplitude is 3 . That lets out the 1st and 3rd choices.
It has to be the 2nd or 4th choice.
Looking at the graph, the y-intercept is at y=6.
The y-intercept is the point where x=0, so f(0)=6.
Test the 2nd choice: f(x) = 3 cos(x) + 3
f(0) = 3 cos(0) + 3
cos(0) = 1 so f(0) = 3 (1) + 3 = 6
Choice-2 is looking good.
Just to be sure, let's check choice-4:
f(x) = 3 sin(x) + 3
f(0) = 3 sin(0) + 3
sin(0) = 0 so f(0) = 3 (0) + 3 = 3
Beautiful ! Choice-4 flopped. The answer is choice-2 .
