/*! 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 Sketch the graph of the function... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Problem 39

Sketch the graph of the function. $$h(x)=\left\\{\begin{array}{ll}4-x^{2}, & x<-2 \\\3+x, & -2 \leq x<0 \\\x^{2}+1, & x \geq 0\end{array}\right.$$

Short Answer

Expert verified
The graph of the function h(x) is split into three parts: a downward facing parabola for x<-2, a straight line rising to the right for -2<=x<0, and an upward facing parabola for x>=0. At x=-2 and x=0, the graph shifts from one piece to another.

Step by step solution

01

Graph the first piece

The function 4-x^2 is a downward facing parabola. To graph the function 4-x^2 for x<-2, start by sketching a downward parabola as if you were sketching the whole function, and then erase the points where x>=-2 since they are not part of this piece of the function.
02

Graph the second piece

The function 3+x is a straight line. To graph the function 3+x for -2<=x<0, start by sketching the straight line as if you were sketching the whole function, and then erase the points where x<-2 and x>=0 since they are not part of this piece of the function.
03

Graph the third piece

The function x^2+1 is an upward facing parabola shifted one unit up. To graph the function x^2+1 for x>=0, start by sketching an upward parabola as if you were sketching the whole function, and then erase the points where x<0 since they are not part of this piece of the function.
04

Check points of change

Check the points of change at x=-2 and x=0 to make sure they match with the definition of the function. Connect the pieces of the graph smoothly to reflect the continuous behavior of the function.

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

Determine whether the statement is true or false. Justify your answer. A function with a square root cannot have a domain that is the set of real numbers.

Find a mathematical model that represents the statement. (Determine the constant of proportionality.) \(F\) is jointly proportional to \(r\) and the third power of \(s\) \((F=4158 \text { when } r=11 \text { and } s=3 .)\)

(a) Write the linear function \(f\) such that it has the indicated function values and (b) Sketch the graph of the function. $$f(-5)=-1, \quad f(5)=-1$$

Write the area \(A\) of a square as a function of its perimeter \(P\).

(a) Write the linear function \(f\) such that it has the indicated function values and (b) Sketch the graph of the function. $$f(1)=4, \quad f(0)=6$$
See all solutions

Recommended explanations on Math Textbooks

Statistics

Read Explanation

Geometry

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Discrete Mathematics

Read Explanation

Applied Mathematics

Read Explanation

Logic and Functions

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.