Answer
See graph.
$(-\infty,\infty)$, $[-\frac{1}{2},\frac{1}{2}]$.
Work Step by Step
Step 1. See graph for $y=-\frac{1}{2}cos(2x)$ with key points.
Step 2. Based on the graph, we can determine the domain as $(-\infty,\infty)$ range as $[-\frac{1}{2},\frac{1}{2}]$.