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The Vertical Line Test

Master the vertical line test with interactive lessons and practice problems! Designed for students like you!

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The Vertical Line Test

Study Guide

Key Definition

A graph represents a function if and only if no vertical line intersects the graph at more than one point.

Important Notes

If a vertical line intersects a graph more than once, the graph is not a function.
The vertical line test is a visual way to determine if a graph represents a function.
$x = 1$ is an example of a vertical line.
Points shown with open circles are not part of the graph and therefore are not counted when applying the vertical line test
Piecewise functions can pass the vertical line test if each piece does not overlap vertically.

Mathematical Notation

$x = k$ represents a vertical line at $x$ equals $k$

$f(x)$ denotes the output value of the function $f$ at the input $x$

Remember to use proper notation when solving problems

Why It Works

The vertical line test works because a function has only one output for each input. If a vertical line crosses the graph at more than one point, it indicates multiple outputs for a single input.

Remember

Use the vertical line test to quickly check if a graph is a function.

Quick Reference

Function Definition:A relation where each input has exactly one output.

Understanding The Vertical Line Test

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Video explanation of this concept

Beginner

Start here! Easy to understand

Beginner Explanation

The vertical line test checks if a graph is a function by ensuring no vertical line intersects the graph more than once.

Practice Problems

Test your understanding with practice problems

Quick Quiz

Single Choice Quiz

Beginner

Which graph passes the vertical line test?

Real-World Problem

Question Exercise

Intermediate

Teenager Scenario

Imagine plotting your daily study hours over a week. Does your graph pass the vertical line test?

Thinking Challenge

Thinking Exercise

Intermediate

Think About This

Consider a graph of your favorite music streaming over time. How would you determine if it passes the vertical line test?

Challenge Quiz

Single Choice Quiz

Advanced

Which of the following graphs represents a function?

Recap

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Review key concepts and takeaways