Answer
Refer to the blue graph below.
Work Step by Step
The parent function of $y= e^{x}$.
Graph the parent function $y=e^x$ to obtain the black graph below.
Note that in the given function $y=e^{|x|}$, the exponent will always be nonnegative.
For example, when $x=-3$, the function becomes:
$y=e^{|-3|}=e^3$.
This means that the graph of the function for $x\lt0$ will just be the reflection about the $y$-axis of the part of the function where $x\gt0$.
Doing this gives the blue graph below.