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