Vertical line test

Definition

The vertical line test is a method used to determine if a graph represents a function. If any vertical line intersects the graph at more than one point, the graph does not represent a function.

5 Must Know Facts For Your Next Test

1. A graph passes the vertical line test if and only if every vertical line intersects the graph at most once.
2. The vertical line test can be used for both continuous and discrete graphs.
3. If a vertical line intersects a graph in more than one place, the relation represented by the graph is not a function.
4. The vertical line test is related to the definition of a function, which states that each input must map to exactly one output.
5. Graphs of functions will always pass the vertical line test.

Review Questions

• What does it mean if a graph fails the vertical line test?
• Can you use the vertical line test on discrete graphs? Explain why or why not.
• Why is passing the vertical line test important for determining whether a relation is a function?

Related terms

Function:

A relation where each input has exactly one output.

Graph:

A visual representation of data or mathematical relationships between variables, typically using axes.

Domain:

The set of all possible input values (independent variable) for which a function is defined.