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