Use the Vertical Line Test

Concept Overview

• The vertical line test is a method used to determine if a curve in the plane is the graph of a function.
• If a vertical line intersects the curve at more than one point, then the curve is not a function.
• This test helps confirm if each input (x-value) has a single output (y-value).

Steps to Perform the Vertical Line Test

1. Draw or visualize a vertical line that moves across the graph.
2. Check the number of intersections as the line moves:
   • If at any vertical position, the line crosses the graph more than once, the graph does not represent a function.
   • If the line never intersects more than once at any position, the graph represents a function.

Applications

• Useful in algebra to quickly verify if an equation could be a function.
• Commonly applied in calculus and other higher-level mathematics.

Importance

• Ensures clarity in defining mathematical relationships.
• Helps avoid errors in interpreting data represented by graphs.