Function Or Not: Vertical Line Test

A graph, too, can easily tell us whether the shown relation is a function or not. This rule is called the Vertical Line Test: if any vertical line that you can draw on top of the graph intersects only once with the curve, then the relation is a function; otherwise, if you can draw a vertical line that intersects twice or more with the curve, then the relation is NOT a function.

Only one intersection with any vertical line - a function ✔
This is a function: each vertical line intersects only ONCE with the blue curve. Specifically, the displayed function is the square function.

This is a function! Miriam Briskman, CC BY-NC 4.0

Two or more intersections with a vertical line - NOT a function ✕
This is NOT a function. We added a red vertical line at x = 1. This vertical line intersects TWICE with the blue curve: once at y = 0, and another time at y = 0.

This is NOT a function. Miriam Briskman, CC BY-NC 4.0

These notes by Miriam Briskman are licensed under CC BY-NC 4.0 and based on sources.