Answer
See graph.
Work Step by Step
Step 1. Given $y=-csc(-\frac{1}{2}\pi x+\frac{\pi}{4})=-csc[-\frac{1}{2}\pi(x-\frac{1}{2})]$, we can find the period $p=\frac{2\pi}{\pi/2}=4$, and phase shift $\phi=\frac{1}{2}$.
Step 2. To plot, start from one period of $y=csc(x)$, shift $\frac{1}{2}$ units to the right, shrink horizontally by a factor of $\frac{2}{\pi}$, reflect across the y-axis, then reflect across the x-axis, and then use the period to repeat the resulting curve. See graph.
