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