Answer
See graph, domain $\{x|x\ne k\pi+\frac{\pi}{4}\}$ (k is an integer), range $(-\infty,-1]\cup[1,\infty)$.
Work Step by Step
1. See graph for $y=csc(x+\frac{\pi}{4})$.
2. We can determine the domain $\{x|x\ne k\pi+\frac{\pi}{4}\}$ (k is an integer), range $(-\infty,-1]\cup[1,\infty)$.