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