Answer
See below.
Work Step by Step
Step 1. To obtain the graph of $f(x)=3^{x-1}$ from $y=3^x$, shift the curve 1 unit to the right. See graph.
Step 2. We can determine the domain is $(-\infty,\infty)$; the range is $(0,\infty)$; and the horizontal asymptote is $y=0$.