Question

Find a function for the graph below.

Answer 1

Answer:

C

Step-by-step explanation:

From the graph you can see that y changes from -2 to 2, so the range of the function is $[-2,2].$

Since the range of the functions $y=\cos x$ and $y=\sin x$ is $[-1,1]$ and the range of the functions $y=k\cos x$ and $y=k\sin x$ is $[-k,k],$  we can state that the correct option is  C: $f(t)=-2\cos 3t.$

Check the value at t=0:

$f(0)=-2\cos 3\cdot 0=-2\cos 0=-2.$