# How do you use the vertical line test to show x=absy is a function?

$y$ is not a function of $x$.
For example, the vertical line $x = 1$ intersects the relation $x = \left\mid y \right\mid$ at two points:
$\left(1 , 1\right)$ and $\left(1 , - 1\right)$
So $y$ is not uniquely determined by $x$.