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 no vertical line intersects it at more than one point.
2. If even one vertical line intersects the graph at multiple points, it fails the test and is not a function.
3. The vertical line test can be applied to any type of graph, including piecewise functions and implicit curves.
4. Graphs of functions that pass the vertical line test include linear functions, quadratic functions, and polynomial functions.
5. Failing the vertical line test means that for some input value $x$, there are multiple output values $y$, which violates the definition of a function.

Review Questions

• How does the vertical line test determine if a graph represents a function?
• What conclusion can you draw if a single vertical line intersects a graph at multiple points?
• Can the vertical line test be used on piecewise functions? Why or why not?

Related terms

Function:

A relation where each input has exactly one output.

Graph: A visual representation of data or mathematical relationships, often in coordinate form.

Piecewise Function: A function composed of multiple sub-functions, each applying to different intervals of the domain.