/*! 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 23 Determine whether the graph of e... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Problem 23

Determine whether the graph of each equation is symmetric with respect to the \(y\) -axis, the \(x\) -axis, the origin, more than one of these, or none of these. $$y=2 x+3$$

Short Answer

Expert verified
The graph of the equation \(y=2x+3\) is not symmetric with respect to the x-axis, the y-axis, or the origin.

Step by step solution

01

Test for symmetry with respect to the y-axis

Replace \(x\) with \(-x\) in the equation, if the equation remains the same then it is symmetric with respect to the y-axis. Replacing \(x\) with \(-x\) gives: \(y=-2x+3\). Thus, the equation is not symmetric about the y-axis because the resulting equation is different from the original.
02

Test for symmetry with respect to the x-axis

Replace \(y\) with \(-y\) in the equation, if the equation remains the same then it is symmetric with respect to the x-axis. Replacing \(y\) with \(-y\) gives: \(-y=2x+3\). Thus, the equation is not symmetric about the x-axis because the resulting equation is different from the original.
03

Test for symmetry with respect to the origin

Replace both \(x\) and \(y\) with \(-x\) and \(-y\) respectively in the equation, if the equation remains the same then it is symmetric with respect to the origin. Replacing \(x\) with \(-x\) and \(y\) with \(-y\) gives: \(-y=-2x-3\). Thus, the equation is not symmetric about the origin because the resulting equation is different from the original.

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

Complete the square and write the equation in standard form. Then give the center and radius of each circle and graph the equation. $$x^{2}+y^{2}+12 x-6 y-4=0$$

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

In your own words, describe how to find the midpoint of a line segment if its endpoints are known.

Complete the square and write the equation in standard form. Then give the center and radius of each circle and graph the equation. $$x^{2}+y^{2}+8 x-2 y-8=0$$

Complete the square and write the equation in standard form. Then give the center and radius of each circle and graph the equation. $$x^{2}+y^{2}-4 x-12 y-9=0$$
See all solutions

Recommended explanations on Math Textbooks

Mechanics Maths

Read Explanation

Discrete Mathematics

Read Explanation

Geometry

Read Explanation

Statistics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Calculus

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.