Answer
See graph.
$(-\infty,\infty)$, $[-6,2]$.
Work Step by Step
Step 1. See graph for $y=4sin(\frac{\pi}{2} x)-2$ with key points or transform from $y=sin(x)$ (shrink horizontally by a factor of $\frac{2}{\pi}$, stretch vertically by a factor of 4, then shift 2 units down.)
Step 2. Based on the graph, we can determine the domain as $(-\infty,\infty)$ range as $[-6,2]$.