Vertical Line Test

Pronunciation: /ˈvɜr.tɪ.kəl laɪn tɛst/ Explain

A vertical line test is used to determine if a relation plotted on a graph is a function or not. To do the vertical line test, graph the relation, and then look at the graph. If anywhere you can place a vertical line passes through the graph at most once, then the relation is a function. If any vertical line passes through the graph more than once, the relation is not a function.

Click on the blue point and drag it to change the figure. Does the vertical line ever cross the graph more than once? Manipulative 1 - Vertical Line Test - Successful Created with GeoGebra.

Move the point over to the far left. Then slowly move it to the far right. How many times does the red vertical line intersect the graph? Since there does not exist at least one vertical line that intersects more than one point, the graph represents a function.

Click on the blue point in the figure and drag it to change the figure. Does the vertical line ever cross the graph more than once? Manipulative 2 - Vertical Line Test - Failure Created with GeoGebra.

Move the point over to the far left. Does the red vertical line intersect the graph? Now move the point to the middle of the manipulative. Does the red vertical line intersect the graph? There are 2 purple intersection points. Since there exists at least one vertical line that intersects more than one point, the graph does not represent a function.

References

1. McAdams, David E.. All Math Words Dictionary, vertical line test. 2nd Classroom edition 20150108-4799968. pg 190. Life is a Story Problem LLC. January 8, 2015. Buy the book

Cite this article as:

McAdams, David E. Vertical Line Test. 12/21/2018. All Math Words Encyclopedia. Life is a Story Problem LLC. https://www.allmathwords.org/en/v/vertlinetest.html.

Image Credits

• All images and manipulatives are by David McAdams unless otherwise stated. All images by David McAdams are Copyright © Life is a Story Problem LLC and are licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.

Revision History

12/21/2018: Reviewed and corrected IPA pronunication. (McAdams, David E.)
12/17/2018: Removed broken links, updated license, implemented new markup, update to new GeoGebra app. (McAdams, David E.)
8/7/2018: Changed vocabulary links to WORDLINK format. (McAdams, David E.)
9/16/2008: Changed images to manipulatives. (McAdams, David E.)
3/11/2008: Added vocabulary link to relation. (McAdams, David E.)
7/12/2007: Initial version. (McAdams, David E.)