Answer
See graph, domain $\{x|x\ne 3\pi k\}$ (where $k$ is an integer), range $(-\infty,-3]U[1,\infty)$.
Work Step by Step
Step 1. See graph for $y=2csc(\frac{1}{3}x)-1$.
Step 2. Based on the graph, we can determine the domain $\{x|x\ne 3\pi k\}$ (where $k$ is an integer), range $(-\infty,-3]U[1,\infty)$.