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