Answer
please see graph (blue curve),
asymptote of $g$:$\quad\quad y=0$
domain of $g=(-\infty,\infty)$
range of $g=(0,\infty)$
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.
$g(x)=2\cdot e^{x}=2\cdot f(x)$
so the graph of $g(x)$ (blue) is obtained by
vertically stretching the graph of f(x) (red)
by a factor of 2.
Reading the graph,
asymptote of $g$:$\quad\quad y=0$
domain of $g=(-\infty,\infty)$
range of $g=(0,\infty)$
