Answer
$y=3 \cos \frac{1}{2}x$
Work Step by Step
Upon inspection, we find that the graph shows a cos function with an amplitude of 3 and a period of $4\pi$.
In the standard equation $y=a \cos bx$, $a$ is the amplitude. Since the amplitude is 3, $a$ is equal to 3. To find the value of $b$, we use the formula:
Step 1: Period$=\frac{2\pi}{b}$
Step 2: $4\pi=\frac{2\pi}{b}$
Step 3: $b=\frac{2\pi}{4\pi}$
Step 4: $b=\frac{1}{2}$
Substituting the values of $a$ and $b$ in the equation $y=a \cos bx$, we find that the equation of the graph is $y=3 \cos \frac{1}{2}x$.