Answer
See graph.
$(-\infty,\infty)$, $[1,2]$.
Work Step by Step
Step 1. See graph for $y=-\frac{1}{2}sin(\frac{\pi}{8}x)+\frac{3}{2}$ with key points or transform from $y=sin(x)$ (stretch horizontally by a factor of $\frac{8}{\pi}$, shrink vertically by a factor of $\frac{1}{2}$, reflect across the x-axis, then shift $\frac{3}{2}$ units up.)
Step 2. Based on the graph, we can determine the domain as $(-\infty,\infty)$ range as $[1,2]$.