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