Answer
The graph of the function $y=e^{|x|}$ is from $(0,\infty)$ and its reflection along y-axis as depicted below:
Work Step by Step
As per piecewise definition of absolute values $y=x$ for $x\geq 0$ and $y=-x$ for $x<0$
Therefore, as per the question, we have $y=e^{x}$ for $x\geq 0$ and $y=e^{-x}$ for $x<0$
The graph of the function $y=e^{|x|}$ is from $(0,\infty)$ and its reflection along y-axis as depicted below:
