Complete Solutions Manual
Precalculus Functions and Graphs
THIRTEENTH EDITION
Earl W. Swokowski
Jeffery A. Cole
Prepared by
Jeffery A. Cole
Australia • Brazil • Mexico • Singapore • United Kingdom • United States
,© 2019 Cengage Learning ISBN: 978-1-337-55235-6
WCN: 01-100-101
Cengage Learning
ALL RIGHTS RESERVED. No part of this work covered by the 20 Channel Center Street
copyright herein may be reproduced, transmitted, stored, or Boston, MA 02210
used in any form or by any means graphic, electronic, or USA
mechanical, including but not limited to photocopying,
recording, scanning, digitizing, taping, Web distribution, Cengage Learning is a leading provider of customized
information networks, or information storage and retrieval learning solutions with office locations around the globe,
systems, except as permitted under Section 107 or 108 of the including Singapore, the United Kingdom, Australia,
1976 United States Copyright Act, without the prior written Mexico, Brazil, and Japan. Locate your local office at:
permission of the publisher. www.cengage.com/global.
Cengage Learning products are represented in
Canada by Nelson Education, Ltd.
For product information and technology assistance, contact us at
Cengage Learning Customer & Sales Support, To learn more about Cengage Learning Solutions,
1-800-354-9706. visit www.cengage.com.
For permission to use material from this text or product, submit Purchase any of our products at your local college store or
all requests online at www.cengage.com/permissions at our preferred online store www.cengagebrain.com.
Further permissions questions can be emailed to
.
, Preface
This manual contains solutions/answers to all exercises in the text Precalculus:
Functions and Graphs, Thirteenth Edition, by Earl W. Swokowski and Jeffery A. Cole. A
Student's Solutions Manual is also available; it contains solutions for the odd-numbered exercises
in each section and for the Discussion Exercises, as well as solutions for all the exercises in the
Review Sections and for the Chapter Tests.
For most problems, a reasonably detailed solution is included. It is my hope that by
merely browsing through the solutions, professors will save time in determining appropriate
assignments for their particular class.
I appreciate feedback concerning errors, solution correctness or style, and manual style—
comments from professors using previous editions have greatly strengthened the ancillary package
as well as the text. Any comments may be sent directly to me at .
I would like to thank: Marv Riedesel and Mary Johnson for accuracy checking of the
new exercises; Andrew Bulman-Fleming, for manuscript preparation; Brian Morris and the late
George Morris, of Scientific Illustrators, for creating the mathematically precise art package; and
Laura Gallus, of Cengage Learning, for checking the manuscript. I dedicate this manual to Carly,
Eli, and Mason, my grandchildren.
Jeffery A. Cole
© 2019 Cengage Learning. All Rights Reserved.
May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
, Table of Contents
1 Topics from Algebra.............................................................................................................................. 1
1.1 Real Numbers • .................................................................................................................. 1
1.2 Exponents and Radicals • ...................................................................................................5
1.3 Algebraic Expressions • ................................................................................................... 10
1.4 Equations • ....................................................................................................................... 19
1.5 Complex Numbers • .........................................................................................................30
1.6 Inequalities • .................................................................................................................... 34
Chapter 1 Review Exercises • .......................................................................................... 42
Chapter 1 Discussion Exercises • .................................................................................... 48
Chapter 1 Test • ............................................................................................................... 51
2 Functions and Graphs..........................................................................................................................55
2.1 Rectangular Coordinate Systems • ................................................................................... 55
2.2 Graphs of Equations • ...................................................................................................... 60
2.3 Lines • .............................................................................................................................. 73
2.4 Definition of Function • ................................................................................................... 82
2.5 Graphs of Functions • ...................................................................................................... 93
2.6 Quadratic Functions • .....................................................................................................109
2.7 Operations on Functions • .............................................................................................. 118
Chapter 2 Review Exercises • ........................................................................................ 130
Chapter 2 Discussion Exercises • .................................................................................. 143
Chapter 2 Test • ............................................................................................................. 146
3 Polynomial and Rational Functions..................................................................................................149
3.1 Polynomial Functions of Degree Greater Than 2 • ........................................................ 149
?3.2 Properties of Division • .................................................................................................. 162
3.3 Zeros of Polynomials • ................................................................................................... 168
3.4 Complex and Rational Zeros of Polynomials • .............................................................. 175
3.5 Rational Functions • ....................................................................................................... 183
3.6 Variation • ...................................................................................................................... 200
Chapter 3 Review Exercises • ........................................................................................ 204
Chapter 3 Discussion Exercises • .................................................................................. 210
Chapter 3 Test • ............................................................................................................. 213
4 Inverse, Exponential, and Logarithmic Functions.......................................................................... 215
4.1 Inverse Functions • .........................................................................................................215
4.2 Exponential Functions • ................................................................................................. 222
4.3 The Natural Exponential Function • .............................................................................. 236
4.4 Logarithmic Functions • ................................................................................................. 244
4.5 Properties of Logarithms • ............................................................................................. 253
4.6 Exponential and Logarithmic Equations • ..................................................................... 261
Chapter 4 Review Exercises • ........................................................................................ 271
Chapter 4 Discussion Exercises • .................................................................................. 279
Chapter 4 Test • ............................................................................................................. 282
© 2019 Cengage Learning. All Rights Reserved.
May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
Precalculus Functions and Graphs
THIRTEENTH EDITION
Earl W. Swokowski
Jeffery A. Cole
Prepared by
Jeffery A. Cole
Australia • Brazil • Mexico • Singapore • United Kingdom • United States
,© 2019 Cengage Learning ISBN: 978-1-337-55235-6
WCN: 01-100-101
Cengage Learning
ALL RIGHTS RESERVED. No part of this work covered by the 20 Channel Center Street
copyright herein may be reproduced, transmitted, stored, or Boston, MA 02210
used in any form or by any means graphic, electronic, or USA
mechanical, including but not limited to photocopying,
recording, scanning, digitizing, taping, Web distribution, Cengage Learning is a leading provider of customized
information networks, or information storage and retrieval learning solutions with office locations around the globe,
systems, except as permitted under Section 107 or 108 of the including Singapore, the United Kingdom, Australia,
1976 United States Copyright Act, without the prior written Mexico, Brazil, and Japan. Locate your local office at:
permission of the publisher. www.cengage.com/global.
Cengage Learning products are represented in
Canada by Nelson Education, Ltd.
For product information and technology assistance, contact us at
Cengage Learning Customer & Sales Support, To learn more about Cengage Learning Solutions,
1-800-354-9706. visit www.cengage.com.
For permission to use material from this text or product, submit Purchase any of our products at your local college store or
all requests online at www.cengage.com/permissions at our preferred online store www.cengagebrain.com.
Further permissions questions can be emailed to
.
, Preface
This manual contains solutions/answers to all exercises in the text Precalculus:
Functions and Graphs, Thirteenth Edition, by Earl W. Swokowski and Jeffery A. Cole. A
Student's Solutions Manual is also available; it contains solutions for the odd-numbered exercises
in each section and for the Discussion Exercises, as well as solutions for all the exercises in the
Review Sections and for the Chapter Tests.
For most problems, a reasonably detailed solution is included. It is my hope that by
merely browsing through the solutions, professors will save time in determining appropriate
assignments for their particular class.
I appreciate feedback concerning errors, solution correctness or style, and manual style—
comments from professors using previous editions have greatly strengthened the ancillary package
as well as the text. Any comments may be sent directly to me at .
I would like to thank: Marv Riedesel and Mary Johnson for accuracy checking of the
new exercises; Andrew Bulman-Fleming, for manuscript preparation; Brian Morris and the late
George Morris, of Scientific Illustrators, for creating the mathematically precise art package; and
Laura Gallus, of Cengage Learning, for checking the manuscript. I dedicate this manual to Carly,
Eli, and Mason, my grandchildren.
Jeffery A. Cole
© 2019 Cengage Learning. All Rights Reserved.
May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
, Table of Contents
1 Topics from Algebra.............................................................................................................................. 1
1.1 Real Numbers • .................................................................................................................. 1
1.2 Exponents and Radicals • ...................................................................................................5
1.3 Algebraic Expressions • ................................................................................................... 10
1.4 Equations • ....................................................................................................................... 19
1.5 Complex Numbers • .........................................................................................................30
1.6 Inequalities • .................................................................................................................... 34
Chapter 1 Review Exercises • .......................................................................................... 42
Chapter 1 Discussion Exercises • .................................................................................... 48
Chapter 1 Test • ............................................................................................................... 51
2 Functions and Graphs..........................................................................................................................55
2.1 Rectangular Coordinate Systems • ................................................................................... 55
2.2 Graphs of Equations • ...................................................................................................... 60
2.3 Lines • .............................................................................................................................. 73
2.4 Definition of Function • ................................................................................................... 82
2.5 Graphs of Functions • ...................................................................................................... 93
2.6 Quadratic Functions • .....................................................................................................109
2.7 Operations on Functions • .............................................................................................. 118
Chapter 2 Review Exercises • ........................................................................................ 130
Chapter 2 Discussion Exercises • .................................................................................. 143
Chapter 2 Test • ............................................................................................................. 146
3 Polynomial and Rational Functions..................................................................................................149
3.1 Polynomial Functions of Degree Greater Than 2 • ........................................................ 149
?3.2 Properties of Division • .................................................................................................. 162
3.3 Zeros of Polynomials • ................................................................................................... 168
3.4 Complex and Rational Zeros of Polynomials • .............................................................. 175
3.5 Rational Functions • ....................................................................................................... 183
3.6 Variation • ...................................................................................................................... 200
Chapter 3 Review Exercises • ........................................................................................ 204
Chapter 3 Discussion Exercises • .................................................................................. 210
Chapter 3 Test • ............................................................................................................. 213
4 Inverse, Exponential, and Logarithmic Functions.......................................................................... 215
4.1 Inverse Functions • .........................................................................................................215
4.2 Exponential Functions • ................................................................................................. 222
4.3 The Natural Exponential Function • .............................................................................. 236
4.4 Logarithmic Functions • ................................................................................................. 244
4.5 Properties of Logarithms • ............................................................................................. 253
4.6 Exponential and Logarithmic Equations • ..................................................................... 261
Chapter 4 Review Exercises • ........................................................................................ 271
Chapter 4 Discussion Exercises • .................................................................................. 279
Chapter 4 Test • ............................................................................................................. 282
© 2019 Cengage Learning. All Rights Reserved.
May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
