Answer
See graph (red), domain $(-\infty,\infty)$, range $(5,\infty)$, horizontal asymptote $y=5$.
Work Step by Step
To obtain the graph of $g(x)=3^{x-1}+5$ from $y=3^x$, shift the curve 1 unit to the right, then shift 5 units up. See graph (red). We can find the domain $(-\infty,\infty)$, range $(5,\infty)$, horizontal asymptote $y=5$.
