Answer
please see image below (f(x)=red curve, g(x)=blue curve),
asymptote of $f:\quad\quad y=0$
asymptote of $g:\quad\quad y=0$
Work Step by Step
Graph $ f(x)=3^{x}\qquad$ (red)
by plotting the points from the table and connecting with a smooth curve.
$g(x)=\displaystyle \frac{1}{3}\cdot 3^{x}=\frac{1}{3}\cdot f(x)$
so the graph of $g(x)$ (blue) is obtained by
vertically shrinking the graph of f(x) by factor $\displaystyle \frac{1}{3}.$
Reading the graph,
asymptote of $f:\quad\quad y=0$
asymptote of $g:\quad\quad y=0$