Teaching Notes 8.4: Using the Vertical Line Test
The vertical line test can be a useful tool to determine if the graph of a relation represents a
function. Students often make mistakes applying the vertical line test to a graph, which leads to
faulty interpretation of the results.- Explain that some relations are functions and other relations are not. If necessary, refer to
8.1: ‘‘Determining if a Relation Is a Function.’’ - Explain that all relations and functions can be graphed in the coordinate plane. The vertical
line test is a way to tell if a relation is a function by looking at its graph. Note that there are
an infinite number of vertical lines that can be drawn in a coordinate plane. Some of these
lines will intersect a graph of a relation and others will not. If there is at least one vertical
line that intersects the graph at two or more points, then the relation is not a function. - Review the information and examples on the worksheet with your students. Emphasize that
a vertical line must intersect the graph only once if the graph is the graph of a function.
EXTRA HELP:
Remember that every vertical line that can possibly be drawn must be considered in order to
determine if a relation is a function.ANSWER KEY:
(1)Function (2)Relation (3)Function (4)Relation
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(Challenge)Alicia is correct. Every horizontal line is a function because every vertical line in
the coordinate plane will intersect a horizontal line exactly once.
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