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