# How do you use the vertical line test to show y=abs(x-3)+abs(x-1) is a function?

Any vertical line is described by an equation of the form $x = k$ for some $k \in \mathbb{R}$.
${y}_{k} = \left\mid k - 3 \right\mid + \left\mid k - 1 \right\mid$
This describes a unique point of intersection $\left(k , {y}_{k}\right)$ between $x = k$ and the curve described by the equation $y = \left\mid x - 3 \right\mid + \left\mid x - 1 \right\mid$
The vertical line test is satisfied: No vertical line intersects the curve described by the equation $y = \left\mid x - 3 \right\mid + \left\mid x - 1 \right\mid$ at more than one point.