# data[].attributes.attachment_link.title
Functions - Cool math Algebra Help Lessons - The Vertical Line Test

# data[].attributes.attachment_link.description
This algebra lesson explains how to use the vertical line test to see if something is a function or not

# data[].attributes.attachment_link.readable_text
The vertical line test is a method that is used to determine whether a given relation is a function or not. The approach is rather simple. Draw a vertical line cutting through the graph of the relation, and then observe the points of intersection.

Why does this work?

The vertical line test supports the definition of a function. That is, every x -value of a function must be paired to a single y -value. If we think of a vertical line as an infinite set of x -values, then intersecting the graph of a relation at exactly one point by a vertical line implies that a single x -value is only paired to a unique value of y.

In contrary, if the vertical line intersects the graph more than once this suggests that a single x -value is being associated with more than one value of y. This condition causes the relation to be "disqualified" or not considered as a function.

For more math videos, click "VIDEOS" on the menu above

So here's the deal!

If a vertical line intersects the graph in all places at exactly one point, then the relation is a function.

Here are some examples of relations that are also functions because they pass the vertical line test.

Cutting or Hitting the Graph at Exactly One Point

Graph of the line f\left( x \right) = x + 1

Graph of the quadratic function (parabola) f\left( x \right) = {x^2} - 2

Graph of the cubic function f\left( x \right) = {x^3}

If a vertical line intersects the graph in some places at more than one point, then the relation is NOT a function.

Here are some examples of relations that are NOT functions because they fail the vertical line test.

Cutting or Hitting the Graph in More Than One Point

Graph of the "sideway" parabola x = y ²

Graph of the relation − x = y ³ y + 2

You might also be interested in: ﻿
Horizontal Line Test

# data[].attributes.attachment_link.description
Vertical Line Test The vertical line test is a method that is used to determine whether a given relation is a function or not. The approach is rather simple. Draw a vertical line cutting through the graph of the relation, and then observe the points of intersection. Why does this work?

# data[].attributes.body
This is due for a grade

# data[].attributes.body
Practice

# data[].attributes.attachment_link.title
IXL | Write a linear equation from a slope and y-intercept | 8th grade math

# data[].attributes.attachment_link.description
Improve your math knowledge with free questions in "Write a linear equation from a slope and y-intercept" and thousands of other math skills.

# data[].attributes.body
We will make a fold -able for notes.

# data[].attributes.body
We will go through this together. Look back over it tonight to be sure you understand.