Vertical Line Test

Pronunciation: /ˈvɜr tɪ kəl laɪn tɛst/ ?

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.

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Manipulative 1: This relation passes the vertical line test. The relation is a function.

Created with GeoGebra.

Click on the blue point in manipulative 1 and drag it to change the figure. 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 is a function.

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Manipulative 2: This relation does not pass the vertical line test. The relation is not a function.

Created with GeoGebra.

Click on the blue point in manipulative 2 and drag it to change the figure. 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 is not a function.

Cite this article as:


Vertical Line Test. 2008-09-16. All Math Words Encyclopedia. Life is a Story Problem LLC. http://www.allmathwords.org/en/v/vertlinetest.html.

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Revision History


2008-09-16: Changed images to manipulatives (McAdams, David.)
2008-03-11: Added vocabulary link to relation (McAdams, David.)
2007-07-12: Initial version (McAdams, David.)

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