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