Answer
Please see below.
Work Step by Step
The graph of the function $g(x)=2e^{\frac{x}{2}}$ (the red graph) is the graph of the function $f(x)=e^x$ (the blue graph) horizontally stretched by $2$ and vertically stretched by $2$.
$x=0$ is the horizontal asymptote for both functions $f$ and $g$.
The domain of the functions $f$ and $g$ are$$D_f=( - \infty, \infty ), \qquad D_g= (- \infty, \infty ).$$The range of the functions $f$ and $g$ are$$R_f= (0, \infty ), \qquad R_g= (0, \infty ).$$
