Answer
This function is symmetric about the $y$-axis
Work Step by Step
$f(x)=2|x|$
$\textbf{Symmetry about the $x$-axis}$
This function has no symmetry about the x-axis, because if it had, it would violate the Vertical Rule Test. Another way to realize this is that changing $f(x)$ by $−f(x)$ does not yield an equivalent function.
$\textbf{Symmetry about the $y$-axis}$
Substitute $x$ by $-x$ in $f(x)$ and simplify:
$f(-x)=2|-x|=2|x|$
Since $f(-x)=f(x)$, the given function is symmetric about the $y$-axis.
$\textbf{Symmetry about the origin}$
It can be seen in the test for $y$-axis symmetry that $f(-x)\ne-f(x)$. Because of this, this function is not symmetric about the origin.
The graph of this function is:
