#### Answer

please see graph (blue curve),
asymptote of $g$:$\quad\quad y=2$
domain of $g=(-\infty,\infty)$
range of $g=(2,\infty)$

#### Work Step by Step

Graph $ f(x)=e^{x}\qquad$ (red, dashed)
by plotting the points from the table and connecting with a smooth curve.
$g(x)=e^{x}+2= f(x)+2$
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 $g=(2,\infty)$