Answer
See graph, domain $\{x|x\ne 2\pi k\}$ (where $k$ is an odd integer), range $(-\infty,-2]U[4,\infty)$.
Work Step by Step
Step 1. See graph for $y=3sec(\frac{1}{4}x)+1$.
Step 2. Based on the graph, we can determine the domain $\{x|x\ne 2\pi k\}$ (where $k$ is an odd integer), range $(-\infty,-2]U[4,\infty)$.