Answer
Please see graph
(and details in the "work step by step" section
Work Step by Step
$g(x)=-3^{x}=-f(x)$
so the graph of g(x) (blue) is obtained by
reflecting the graph of f(x) (red)
about the x-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 (-\infty ,0)$
