# How do you decide whether the relation │2y│ = 4x defines a function?

This defines x as a single-valued function of y for all values of y. $x \ge 0$. The graph is the pair of radial lines, from the origin, in the 1st and 4th quadrants, with slopes $\pm 2$.
$x \ge 0$. The equation can be separated into $x = - 2 y$, y<0 and x=2y, y>0.
x is a single-valued function of y. For every x > 0, there are two $\pm y$. values.
The graph is the pair of radial lines, from the origin, in the 1st and 4th quadrants, with slopes $\pm 2$.