/*! 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 39 Determine whether each function ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Problem 39

Determine whether each function is even, odd, or neither. Then determine whether the function's graph is symmetric with respect to the \(y\) -axis, the origin, or neither. $$g(x)=x^{2}+x$$

Short Answer

Expert verified
The function \(g(x)=x^2 + x\) is neither even nor odd. The graph of this function is also not symmetric with respect to either the y-axis or the origin.

Step by step solution

01

Substituting \(-x\) into the function

Substitute \(-x\) into each \(x\) in the function \(g(x)\). Doing this, we get \(g(-x) = (-x)^2 + -x = x^2 - x.\)
02

Comparison

Now compare the function \(g(x)=x^2 + x\) with the new function \(g(-x)=x^2 - x\). They are not the same, so we know it's not even. And \(g(-x)\) is not exactly \(g(x)\) with a \(-\) sign at the front, so it is also not odd. Hence, the function is neither even nor odd.
03

Graph Symmetry

We've already found that \(g(x)\) is neither an even nor an odd function. This means the graph of \(g(x)\) is neither symmetric about the y-axis (which is characteristic of even functions) nor about the origin (which is characteristic of odd functions).

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

Explain how to find the difference quotient of a function \(f\) \(\frac{f(x+h)-f(x)}{h},\) if an equation for \(f\) is given.

Complete the square and write the equation in standard form. Then give the center and radius of each circle and graph the equation. $$x^{2}+y^{2}-10 x-6 y-30=0$$

Find and simplify the difference quotient $$\frac{f(x+h)-f(x)}{h}, h \neq 0$$for the given function. $$f(x)=\sqrt{x-1}$$

Here is the Federal Tax Rate Schedule \(X\) that specifies the tax owed by a single taxpayer for a recent year. (TABLE CANNOT COPY) The preceding tax table can be modeled by a piecewise function, where \(x\) represents the taxable income of a single taxpayer and \(T(x)\) is the tax owed: $$T(x)=\left\\{\begin{array}{ccc} 0.10 x & \text { if } & 0379,150 \end{array}\right.$$ Use this information to solve. Find and interpret \(T(20,000)\)

Determine whether each relation is a function. Give the domain and range for each relation. a. \(\\{(1,6),(1,7),(1,8)\\}\) b. \(\\{(6,1),(7,1),(8,1)\\}\) (Section \(1.2,\) Example 2 )
See all solutions

Recommended explanations on Math Textbooks

Decision Maths

Read Explanation

Geometry

Read Explanation

Statistics

Read Explanation

Logic and Functions

Read Explanation

Pure Maths

Read Explanation

Probability and Statistics

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.