/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 72 What is the horizontal line test... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 2: Problem 72

What is the horizontal line test and what does it indicate?

Short Answer

Expert verified
The horizontal line test is a method used to determine if a function is injective (one-to-one). This is done by drawing a horizontal line through the graph of the function. If the line intersects the graph at more than one point, the function is not injective. The test indicates whether every input to the function will result in a unique output.

Step by step solution

01

Definition of the Horizontal Line Test

The Horizontal Line Test is a method used in mathematics to determine whether a function is injective or not. A function is said to be injective if every element of the function's domain maps to a unique element of its range.
02

Application of the Horizontal Line Test

To apply the horizontal line test, a horizontal line is drawn through the graph of the function. If at any point the horizontal line intersects the graph at more than one point, the function is not injective. In other words, if it is possible for the horizontal line to touch the graph in more than one place, the function has more than one y value for at least one x value, which contradicts the definition of an injective function.
03

Indication of the Horizontal Line Test

The Horizontal Line Test effectively tells us whether a function is injective or not. If a function passes the Horizontal Line Test, it means that the function is injective, and every input to the function will result in a unique output. If a function fails the Horizontal Line Test, it is not injective, indicating that there is an input for which there are multiple outputs.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Describe how to find the inverse of a one-to-one function.

Use a graphing utility to graph the function. Use the graph to determine whether the function has an inverse that is a function (that is, whether the function is one-to-one). $$ f(x)=(x-1)^{3} $$

Use a graphing utility to graph the function. Use the graph to determine whether the function has an inverse that is a function (that is, whether the function is one-to-one). $$ f(x)=-\sqrt{16-x^{2}} $$

How can a graphing utility be used to visually determine if two functions are inverses of each other?

What must be done to a function's equation so that its graph is reflected about the \(y\) -axis?
See all solutions

Recommended explanations on Math Textbooks

Mechanics Maths

Read Explanation

Pure Maths

Read Explanation

Probability and Statistics

Read Explanation

Logic and Functions

Read Explanation

Decision Maths

Read Explanation

Discrete Mathematics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.