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=$1
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.
$g(x)=(\displaystyle \frac{1}{2})^{x}+1=f(x)+1$
so the graph of $g(x)$ (blue) is obtained by
shifting the graph of f(x) up by 1 unit.
Reading the graph,
asymptote of $f:\quad\quad y=0$ (yellow dashed)
asymptote of $g:\quad\quad y=$1 (green dashed)
