Answer
domain $(-\infty,\infty)$, range $(0,\infty)$
See graph.
Work Step by Step
To graph function $f(x)=(\frac{1}{3})^{-x-2}=(\frac{1}{3})^{-(x+2)}$, start from $y=(\frac{1}{3})^x$, reflect the curve across the y-axis, then shift 2 units to the left.
For $f(x)$, we have domain $(-\infty,\infty)$, range $(0,\infty)$
See graph.