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Vertical line test, Horizontal line test, One-to-one function

If no two different points in a graph have the same first coordinate, this means that vertical lines cross the graph at most once. This is known as the vertical line test. Graphs that pass the vertical line test are graphs of functions.

If no two different points in a graph have the same second coordinate, this means that horizontal lines cross the graph at most once. This is known as the horizontal line test. Functions whose graphs pass the horizontal line test are called one-to-one.

Graphs that pass both the vertical line and horizontal line tests are one-to-one functions. These are exactly those functions whose inverse relation is also a function. One-to-one functions have an inverse.

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Function, not one-to-one
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Not a function
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One-to-one function
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One-to-one function


A B C D E F G H I J K L M N O P Q R S T U V W X Y Z


Inverse function


Copyright © 2006 Darel Hardy, Fred Richman, Carol Walker, Robert Wisner. All rights reserved. Except upon the express prior permission in writing, from the authors, no part of this work may be reproduced, transcribed, stored electronically, or transmitted in any form by any method.

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