College Algebra 7th Edition

Published by Brooks Cole
ISBN 10: 1305115546
ISBN 13: 978-1-30511-554-5

Chapter 2, Functions - Section 2.8 - One-to-One Functions and their Inverses - 2.8 Exercises - Page 261: 1


different, Horizontal Line

Work Step by Step

A function $f$ is one-to-one if different inputs produce DIFFERENT outputs. A one-to-one function only exists if for every y-value, it only has only one x-value. In this question, that means for every input, there can only be one output from the system and hence, different inputs produce different outputs. You can tell from the graph that a function is one-to-one by using the HORIZONTAL LINE Test. The Horizontal Line Test is a test where a horizontal line is drawn at any point on the graph of your function, and it must not cross any part of your graph two or more times, because it would mean that you have two x-values for the same y-value. From this, you would be able to conclude that your function is not one-to-one.
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