Answer
See graph.
$(-\infty,\infty)$, $[-1,2]$.
Work Step by Step
Step 1. See graph for $y=-\frac{3}{2}cos(\frac{\pi}{4}x)+\frac{1}{2}$ with key points or transform from $y=cos(x)$ (stretch horizontally by a factor of $\frac{4}{\pi}$, stretch vertically by a factor of $\frac{3}{2}$, reflect across the x-axis, then shift $\frac{1}{2}$ unit up.)
Step 2. Based on the graph, we can determine the domain as $(-\infty,\infty)$ range as $[-1,2]$.
