Answer
$\color{blue}{y=\cos{(\frac{1}{2}x)}+1}$ or $\color{blue}{y=1+\cos{(\frac{1}{2}x)}}$
Work Step by Step
RECALL:
The cosine function $y=\cos{(bx)}$ has
(i) a period of $\frac{2\pi}{b}$;
(ii) an amplitude of $1$; and
(iii) a range of $[-1, 1]$
The given graph looks like the cosine function but has a period of $4\pi$.
Thus,
$4\pi=\frac{2\pi}{b}
\\4\pi{b}=2\pi
\\b=\frac{2\pi}{4\pi}
\\b=\frac{1}{2}$
Note that the given graph has the range $[0, 2]$.
This means that the graph of the function $y=\cos{(bx)}$ was shifted vertically one unit upward.
Therefore, the equation of the function whose graph is given is:
$\color{blue}{y=\cos{(\frac{1}{2}x)}+1}$
