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