Answer
$y=-2 + \csc{x}$
Work Step by Step
The graph has a period of $2\pi$ and looks similar to the graph of the basic cosecant function.
Notice, however, that instead of having the vertices at $(\frac{\pi}{2}, 1)$ and $(\frac{3\pi}{2}, -1)$, the vertices of the ggiven graph are at $(\frac{\pi}{2}, -1)$ and $\frac{3\pi}{2}, -3)$.
This means that the given graph involves a 2-unit downward shift of the parent function $y=\csc{x}$.
Therefore, the equation of the function whose graph is given is $y=\csc{x} -2$ or $y=-2 + \csc{x}$.
