Answer
please see image below (f(x)=red curve, g(x)=blue curve),
asymptote of $f:\quad\quad y=0$
asymptote of $g:\quad\quad y=$2
Work Step by Step
Graph $ f(x)=(\displaystyle \frac{1}{2})^{x}\qquad$ (red)
by plotting the points from the table and connecting with a smooth curve.
$g(x)=(\displaystyle \frac{1}{2})^{x-1}+2=f(x-1)+2$
so the graph of $g(x)$ (blue) is obtained by
shifting the graph of f(x) right by 1 unit, $f(x-1)$ (green dashed).
then, shifting up by 2 units, $f(x-1)+2$, (blue) .
Reading the graph,
asymptote of $f:\quad\quad y=0$ (yellow, dashed)
asymptote of $g:\quad\quad y=$2 (black, dashed