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