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