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