/*! 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 17 Determine whether the graph of e... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Problem 17

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. $$y=x^{2}+6$$

Short Answer

Expert verified
The graph of the equation \(y = x^{2} + 6\) is symmetric with respect to the y-axis, but it is not symmetric with respect to the x-axis or the origin.

Step by step solution

01

Check Symmetry with respect to Y-Axis

The equation \(y = x^{2}+6\) becomes \(y = (-x)^{2}+6\) when \(x\) is replaced with \(-x\). This simplifies to \(y = x^{2}+6\), which is the original equation, so the graph is symmetric with respect to the y-axis.
02

Check Symmetry with respect to X-Axis

Replace \(y\) in the equation \(y = x^{2}+6\) with \(-y\). This gives \(-y = x^{2}+6\), which is not identical to the original equation after simplifying, so the graph is not symmetric with respect to the x-axis.
03

Check Symmetry with respect to the Origin

Replace \(x\) with \(-x\) and \(y\) with \(-y\) in the equation \(y = x^{2}+6\). This results in \(-y = (-x)^{2}+6\), which simplifies to \(-y = x^{2}+6\). This is not identical to the original equation, so the graph is not symmetric with respect to the origin.

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. $$x^{2}+y^{2}+8 x-2 y-8=0$$

The regular price of a computer is \(x\) dollars. Let \(f(x)=x-400\) and \(g(x)=0.75 x\) a. Describe what the functions \(f\) and \(g\) model in terms of the price of the computer. b. Find \((f \circ g)(x)\) and describe what this models in terms of the price of the computer. c. Repeat part (b) for \((g \circ f)(x)\) d. Which composite function models the greater discount on the computer, \(f^{\circ}\) g or \(g \circ f\) ? Explain.

Will help you prepare for the material covered in the next section. Find the perimeter and the area of each rectangle with the given dimensions: a. 40 yards by 30 yards b. 50 yards by 20 yards.

A telephone company offers the following plans. Also given are the piecewise functions that model these plans. Use this information to solve. Plan \(A\) \(\cdot \$ 30\) per month buys 120 minutes. \(\cdot\) Additional time costs \(\$ 0.30\) per minute. $$C(t)=\left\\{\begin{array}{ll}30 & \text { if } 0 \leq t \leq 120 \\\30+0.30(t-120) & \text { if } t>120 \end{array}\right. $$ Plan \(B\) \(\cdot \ 40\) per month buys 200 minutes. \(\cdot\) Additional time costs \(\$ 0.30\) per minute. $$ C(t)=\left\\{\begin{array}{ll} 40 & \text { if } 0 \leq t \leq 200 \\\ 40+0.30(t-200) & \text { if } t>200 \end{array}\right. $$ Simplify the algebraic expression in the second line of the piecewise function for plan A. Then use point-plotting to graph the function.

Use a graphing utility to graph each circle whose equation is given. Use a square setting for the viewing window. $$x^{2}+10 x+y^{2}-4 y-20=0$$
See all solutions

Recommended explanations on Math Textbooks

Calculus

Read Explanation

Geometry

Read Explanation

Probability and Statistics

Read Explanation

Statistics

Read Explanation

Decision Maths

Read Explanation

Applied 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.