Answer
See graph (red).
domain $(-\infty,0]$, range $[-2,\infty)$.
Work Step by Step
Step 1. To obtain the graph of $h(x)=\sqrt {-x}-2$ from $y=\sqrt x$, reflect the curve across the y-axis, then shift 2 units down. See graph (red).
Step 2. We can find the domain $(-\infty,0]$ and the range $[-2,\infty)$.