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