Answer
$\color{blue}{y=0.5\cos(2x)}$
Work Step by Step
The y-values vary from $−0.5$ to $0.5$.
This means that the amplitude:
$\frac{0.5-(-0.5)}{2}=\frac{1}{2}=0.5$.
The given graph looks like a cosine function with no reflection about the x-axis.
This means that the value of $a$ is positive.
Since the amplitude is $|a|$ and is known to be $0.5$, then $a=0.5$.
Thus, the tentative equation of the function whose graph is given is $y=0.5\cos(bx)$.
The period of the cosine function is $\frac{2\pi}{b}$.
The given graph clearly shows that the period of the function is $\pi$.
Thus,
$\frac{2\pi}{b}=\pi
\\2\pi=b{\pi}
\\\frac{2\pi}{\pi}=\frac{b{\pi}}{\pi}
\\2=b$
Therefore, the equation of the function whose graph is given is $\color{blue}{y=0.5\cos(2x)}$.
