Functions and Function Notation: Learn It 2

Using the Vertical Line Test

The vertical line test can be used to determine whether a graph represents a function. If we can draw any vertical line that intersects a graph more than once, then the graph does not define a function because a function has only one output value for each input value.

Three graphs visually showing what is and is not a function.

vertical line test

Determines whether a graph represents a function. To “pass” the vertical line test, a curve should only intersect a vertical line once for every input.

Which of the graphs represent(s) a function [latex]y=f\left(x\right)?[/latex]
Graph of a polynomial.

To determine if a relation is a function:

  • From points, a table, or a mapping: [latex]x[/latex] cannot repeat for different values of [latex]y[/latex]
  • From a graph: use the vertical line test