Answer
please see graph,
asymptote of $g$:$\quad\quad y=2$
domain of $g=(-\infty,\infty)$
range of $g=(2,\infty)$
Work Step by Step
Graph $ f(x)=2^{x}\qquad$ (red, dashed)
by plotting the points from the table and connecting with a smooth curve.
$g(x)=2^{x}+2=f(x)+2$,
so the graph of g(x) (blue) is obtained by
shifting the graph of f(x) (red) up by 2 units.
Reading the graph,
asymptote of $g$:$\quad\quad y=2$
domain of $g=(-\infty,\infty)$
range of $g=(2,\infty)$
