/*! 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 131 What must be done to a function'... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Problem 131

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

Short Answer

Expert verified
To reflect a function's graph about the \(x\)-axis, change the function's equation from \(f(x)\) to \(-f(x)\).

Step by step solution

01

Understand Reflection

Reflection of a graph about the \(x\)-axis means that the position of every point of the original graph is reversed concerning the \(x\)-axis, i.e., the sign of the \(y\)-coordinate of every point on the original graph changes.
02

Implementing Reflection

To apply reflection to a function's equation, one needs to change the sign of the function. If the original function's equation is \(f(x)\), then the reflected function's equation will be \(-f(x)\). This way, for every \(x\), the sign of the corresponding \(y\)-value changes, thus reflecting the graph about the \(x\)-axis.

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

Sketch the graph of \(f\) using the following properties. (More than one correct graph is possible.) \(f\) is a piecewise function that is decreasing on \((-\infty, 2), f(2)=0, f\) is increasing on \((2, \infty),\) and the range of \(f\) is \([0, \infty)\)

What is a piecewise function?

Solve for \(A: C=A+A r\) (Section P.7, Example 5 )

Use a graphing utility to graph each function. Use \(a[-5,5,1]\) by [-5,5,1] viewing rectangle. Then find the intervals on which the function is increasing, decreasing, or constant. $$h(x)=|x-2|+|x+2|$$

Use a graphing utility to graph each circle whose equation is given. Use a square setting for the viewing window. $$x^{2}+y^{2}=25$$
See all solutions

Recommended explanations on Math Textbooks

Pure Maths

Read Explanation

Discrete Mathematics

Read Explanation

Applied Mathematics

Read Explanation

Statistics

Read Explanation

Probability and Statistics

Read Explanation

Decision Maths

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.