## University Calculus: Early Transcendentals (3rd Edition)

$\mathrm{Remember:}\$ We can consider vertical line test to see if the graph is a function of $\ x\$ or not. If a vertical line, let's say $\ \ x=a\ \$ intersects the graph at any two points, the graph would not be a function of $\ x.\$ In both these cases, there exist a real number $\ a\$ for which the vertical line $\ x=a\$ intersects the graphs of $\ |y|=x\$ and $\ |y|=|x|\$ in two points. So, they both are not functions of $\ x.$ $\mathrm{See\:the\:graphs\:below.}$
$a).$ Graph of $\ \ |y|=x\ \$ is the same as the graph of $\ \ y=|x|\ \$ but with the switched $\ x\$ and $\ y\mathrm{-axis}.$ $b).$ Graph of $\ \ y^2=x^2\ \$is the same as the graph of $\ \ |y|=|x|.\ \$ You can also graph functions $\ y=|x|\$ and $\ y=-|x|\$ combined to get the same graph.