Answer
See graph.
domain $(-\infty,\infty)$, range $(-\infty,7)$, H.A. $y=7$.
Work Step by Step
Step 1. To obtain the graph of $f(x)=7-3e^{2x}$ from $y=e^x$, compress the curve horizontally by a factor of 1/2, stretch vertically by a factor of 3, reflect across the x-axis, then shift 7 units up. See graph.
Step 2. We can determine the domain $(-\infty,\infty)$, range $(-\infty,7)$, horizontal asymptote H.A. $y=7$.
