Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 2: Q. 6 (page 100)

True or False The cube function is odd and is increasing on the interval (-∞,∞).

Short Answer

Expert verified

The statement 'The cube function is odd and is increasing on the interval (-∞,∞).' is true.

Step by step solution

01

Step 1. Given information

We have been given a statement 'The cube function is odd and is increasing on the interval (-∞,∞).'

We have to tell whether this statement is true or false.

02

Step 2. Check for the odd function

The cube function is f(x)=x3.

Find f(-x).

f(-x)=(-x)3 f(-x)=-x3f(-x)=-f(x)

Therefore, the function is odd.

03

Step 3. Analyze the graph of cube function

The graph of cube function is:

It is clear from the graph that the cube function is increasing everywhere.

Therefore, the given statement is true.

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.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

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

In Problems 7–18, match each graph to one of the following functions:

A.y=x2+2B.y=-x2+2C.y=x+2D.y=-x+2E.y=(x-2)2F.y=-(x+2)2G.y=x-2H.y=-x+2I.y=2x2J.y=-2x2K.y=2xL.y=-2x

Concepts and Vocabulary

A function f is ___________ on an open interval I if, for any choice of x1 and x2 in I, withx1<x2wehavef(x1)<f(x2)

In Problems 7–18, match each graph to one of the following functions:

A.y=x2+2B.y=-x2+2C.y=x+2D.y=-x+2E.y=(x-2)2F.y=-(x+2)2G.y=x-2H.y=-x+2I.y=2x2J.y=-2x2K.y=2xL.y=-2x

Write the point–slope form of the line with slope 5 containing the point (3, -2).

In Problems 33– 44, determine algebraically whether each function is even, odd, or neither.

h(x)=-x33x2-9
See all solutions

Recommended explanations on Math Textbooks

Probability and Statistics

Read Explanation

Decision Maths

Read Explanation

Pure Maths

Read Explanation

Mechanics Maths

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

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.

Sign-up for free