Answer
Please see graph $\\$
(and details in the "work step by step" section
Work Step by Step
$g(x)=(\displaystyle \frac{1}{2})^{-x}=f(-x)$
so the graph of g(x) (blue) is obtained by
reflecting the graph of f(x) (red)
about the $y$-axis.
Reading the graph,
asymptote of $ f:\quad y=0$
asymptote of $ g:\quad y=0$
domain of $ f:\quad (-\infty,\ \infty)$
range of $ f:\quad (0,\infty$
domain of $ g:\quad$ $(-\infty,\ \infty)$
range of $ g:\quad (0,\infty)$
