We have to find the equation of the function graphed.
We start noticing that the maximum value of the function happens for x=0, which tell us that is a cosine function with no phase offset.
The amplitude is 1, as the function range is [-3,-1] and the amplitude is half the difference between the maximum and minimum value.
The vertical shift is 2 units down, as the pure cosine function average a value of 0 and this function averages a value of -2.
Finally, we have to find the period. The function repeats itself in periods of 2π/5. So we can find the period as:
[tex]\begin{gathered} \cos (T\cdot\frac{2\pi}{5})=\cos (2\pi) \\ 2\pi\cdot\frac{T}{5}=2\pi \\ \frac{T}{5}=1 \\ T=5 \end{gathered}[/tex]The function is:
[tex]y=\cos (5x)-2[/tex]Answer: the function is y = cos(5x)-2
