Answer:
y = cos(4x)
Explanation:
Given a cosine function in the below form;
[tex]y=a\cos (bx)[/tex]where;
Amplitude = |a|
Period = 2pi / |b|
Looking at the given graph, we can see that the amplitude(a) = 1, and the period is pi/2.
Let's go ahead and determine b as seen below;
[tex]\begin{gathered} \text{Period}=\frac{2\pi}{|b|} \\ \frac{\pi}{2}=\frac{2\pi}{|b|} \\ |b|=\frac{2\pi\times2}{\pi} \\ |b|=4 \\ b=4 \end{gathered}[/tex]Since a = 1 and b = 4, the function whose graph is given can be written as;
[tex]y=\cos (4x)[/tex]