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