#### Answer

$\color{blue}{y=2 \tan{(\frac{\pi}{2})}}$

#### Work Step by Step

The graph looks like that of the basic tangent function $y=\tan{x}$.
However, the period of the given function is $2\pi$, while that of the basic tangent function is $\pi$.
RECALL:
The period of the tangent function $y=\tan{(bx)}$ is $\frac{\pi}{b},b\gt 0$.
Thus,
$2\pi=\frac{\pi}{b}
\\2b\pi=\pi
\\\frac{2b\pi}{2\pi}=\frac{\pi}{2\pi}
\\b=2$
Thus, the tentative equation of the function whose graph is given is $y=a\cdot \tan{(\frac{\pi}{2})}$.
The given graph contains the point $(\frac{\pi}{2}, 2)$.
Substituting the x and y values of this point into the tentative equation above gives:
$y=a \cdot \tan{(\frac{\pi}{2})}
\\2=a \cdot \tan{(\frac{\frac{\pi}{2}}{2})}
\\2=a \cdot \tan{\frac{\pi}{4}}
\\2=a \cdot 1
\\2=a$
Therefore, the equation of the the function whose graph is shown is $\color{blue}{y=2 \tan{(\frac{\pi}{2})}}$.