Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 2: Q. 91 (page 92)

How many x-intercepts can a function defined on an interval have if it is increasing on that interval? Explain.

Short Answer

Expert verified

A function can be defined on an interval and increasing on that interval if it has at most onex-intercept.

Step by step solution

01

Step 1. Given Information

The x-intercept is the point where a line crosses the x-axis. We have to find the x-intercepts where a function is defined on an interval and increasing on that interval.

02

Step 2. Explaining

Let's say that the function f(x)is increasing on the interval x1,x2 and if the function has more than one x-intercepts, the function tends to decrease for some interval between x1,x2. Thus, a function can be defined on an interval and increasing on that interval if it has at most one x-intercept.

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

True or False If no domain is specified for a function f, then the domain of fis taken to be the set of real numbers.

If f(x)=x+1and g(x)=x3, then____________ =x3-(x+1).

match each graph to its function.

A. Constant function

B. Identity function

C. Square function

D. Cube function

E. Square root function

F. Reciprocal function

G. Absolute value function

H. Cube root function

Consider the equation

y=1ifxisrational0ifxisirrational

Is this a function? What is its domain? What is its range? What is its y-intercept, if any? What are its x-intercepts, if any? Is it even, odd, or neither? How would you describe its graph?

If f(x)=-3xifx<-10ifx=-12x2+1ifx>-1

Find: (a)f(-2) and (b) f(-1) (c)f(0)
See all solutions

Recommended explanations on Math Textbooks

Calculus

Read Explanation

Applied Mathematics

Read Explanation

Pure Maths

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Logic and Functions

Read Explanation

Discrete 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.

Sign-up for free