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