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Find a function for the graph below.

Find a function for the graph below.-example-1

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Answer:

C

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.

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