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
 McAdams, David E.. All Math Words Dictionary, vertical line test. 2nd Classroom edition 201501084799968. 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. http://www.allmathwords.org/en/v/vertlinetest.html.
Image Credits
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.)