Don't try to draw curve for this function.just know the nature of curve and then eliminate options.
Nature 1) Here we have mod to x : $|x|$ , which means graph would be identical in both $+ve$ x-axis and $-ve$ x-axis. in other words mirror image with respect to y-axis. All options are satisfying this property so know some other nature.
Nature 2) at $x=0$ $y$ would become $0$ so in that way eliminate option B and D.
Nature 3) See if y can be negative or not. To get $-ve$$y$ the power of $e$ must be negative.But see power of $e$ is function of mod , and Mod always result in $+ve$ value so this shows $y$ can't be negative so eliminate A.
in that way only C left , hence answer.