Answer
$y = -csc~2x$
The asymptotes have the form $x = \frac{\pi}{2}n$, for any integer $n$. The period is $\pi$.
We can see the graph below.
Work Step by Step
$y = -csc~2x$
When $x = -\frac{\pi}{2}$, then $y = -csc~(-\pi)~~$ (which is undefined)
When $x = -\frac{\pi}{4}$, then $y = -csc~(-\frac{\pi}{2}) = 1$
When $x = 0$, then $y = -csc~0$ (which is undefined)
When $x = \frac{\pi}{4}$, then $y = -csc~\frac{\pi}{2} = -1$
When $x = \frac{\pi}{2}$, then $y = -csc~\pi~~$ (which is undefined)
The asymptotes have the form $x = \frac{\pi}{2}n$, for any integer $n$. The period is $\pi$.
We can see the graph below.
