Answer
The graph is symmetric with respect to the $x$-axis, but not with respect to the $y$-axis and origin.
Work Step by Step
$|y| - x = 3$
The graph of an equation in $x$ and $y$ is symmetric with respect to the $y$-axis when replacing $x$ by $-x$ yields an equivalent equation.
If $|y| - x = 3$ then $|y| + x \ne 3$
The graph of an equation in $x$ and $y$ is symmetric with respect to the $x$-axis when replacing $y$ by $-y$ yields an equivalent equation.
$|y|$ means $-y = y$ so nothing changes to $y$ meaning nothing changes in the equation.
The graph of an equation in $x$ and $y$ is symmetric with respect to the origin when replacing $x$ by $-x$ and $y$ by $-y$ yields an equivalent equation.
As explained before nothing changes to $y$ but something changes to $x$ so the resulting equation is not equivalent to the original.
