Answer
domain: $(-\infty,\infty)$
range: $(3,\infty)$
asymptote: $y=3 $
Work Step by Step
1. Start with graphing $f_{1}(x)=2^{x}$
as a parent function (blue, dashed on the image below)
Select several values for x, calculate $3^{x}$ for each,
plot the points and connect with a smooth curve)
2.
$g(x)=2^{x}+3=f_{1}(x)+3$
The graph of $g$ (red) is obtained from the graph of $f_{1}(x)$ by
$f(x)=f_{1}(x$)$+3$, shifting up by $3$ units.
domain: $(-\infty,\infty)$
range: $(3,\infty)$
asymptote: $y=3$
