Answer
$y = csc~(x-\frac{\pi}{4})$
We can see the graph below.
Work Step by Step
$y = csc~(x-\frac{\pi}{4})$
When $x = -\frac{3\pi}{4}$, then $y = csc~(-\pi)$ (which is undefined)
When $x = -\frac{\pi}{4}$, then $y = csc~(-\frac{\pi}{2}) = -1$
When $x = \frac{\pi}{4}$, then $y = csc~0$ (which is undefined)
When $x = \frac{3\pi}{4}$, then $y = csc~(\frac{\pi}{2}) = 1$
When $x = \frac{5\pi}{4}$, then $y = csc~2\pi$ (which is undefined)
We can see the graph below.
