INSTRUCTOR’S SOLUTIONS
M
MANUAL
PR
TIM BRITT
Jackson State Community College
ES
COLLEGE ALGEBRA
E NHANCED WITH G RAPHING U TILITIES
SI
EIGHTH EDITION
VE
Michael Sullivan
Chicago State University
G
Michael Sullivan III
Joliet Junior College
R
AD
ES
,M
PR
ES
Please contact https://support.pearson.com/getsupport/s/contactsupport with any queries on this content.
The author and publisher of this book have used their best efforts in preparing this book. These efforts include
the development, research, and testing of the theories and programs to determine their effectiveness. The author
SI
and publisher make no warranty of any kind, expressed or implied, with regard to these programs or the
documentation contained in this book. The author and publisher shall not be liable in any event for incidental or
consequential damages in connection with, or arising out of, the furnishing, performance, or use of these
programs.
VE
Reproduced by Pearson from electronic files supplied by the author.
Copyright © 2021, 2017, 2013 Pearson Education, Inc.
Publishing as Pearson, 21 River Street, Hoboken, NJ 07030. All rights reserved
All rights reserved. Manufactured in the United States of America. This publication is protected by copyright,
G
and permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval
system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or
otherwise. For information regarding permissions, request forms, and the appropriate contacts within the
Pearson Education Global Rights and Permissions department, please visit www.pearsoned.com/permissions/.
R
AD
ISBN-13: 978-0-13-581186-3
ISBN-10: 0-13-581186-4
ES
, Table of Contents
Chapter R Review
M
R.1 Real Numbers ............................................................................................................................1
R.2 Algebra Essentials .....................................................................................................................5
R.3 Geometry Essentials ................................................................................................................11
R.4 Polynomials .............................................................................................................................16
PR
R.5 Factoring Polynomials ............................................................................................................23
R.6 Synthetic Division ...................................................................................................................28
R.7 Rational Expressions ...............................................................................................................30
R.8 nth Roots; Rational Exponents ................................................................................................40
Chapter 1 Graphs, Equations, and Inequalities
ES
1.1 Graphing Utilities; Introduction to Graphing Equations.........................................................50
1.2 Solving Equations Using a Graphing Utility; Linear and Rational Equations .......................57
1.3 Quadratic Equations ................................................................................................................71
1.4 Complex Numbers; Quadratic Equations in the Complex Number System ...........................90
1.5 Radical Equations; Equations Quadratic in Form; Absolute Value Equations;
Factorable Equations ...............................................................................................................96
1.6 Problem Solving: Interest, Mixture, Uniform Motion, Constant Rate Job Applications......117
SI
1.7 Solving Inequalities...............................................................................................................125
Chapter Review .............................................................................................................................137
Chapter Test...................................................................................................................................147
Chapter Projects .............................................................................................................................151
VE
Chapter 2 Graphs
2.1 The Distance and Midpoint Formulas ...................................................................................152
2.2 Intercepts; Symmetry; Graphing Key Equations ..................................................................165
2.3 Lines ......................................................................................................................................182
2.4 Circles ...................................................................................................................................200
2.5 Variation................................................................................................................................215
Chapter Review .............................................................................................................................220
G
Chapter Test ...................................................................................................................................226
Cumulative Review .......................................................................................................................228
Chapter Projects .............................................................................................................................230
R
Chapter 3 Functions and Their Graphs
3.1 Functions ...............................................................................................................................231
3.2 The Graph of a Function .......................................................................................................249
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3.3 Properties of Functions .........................................................................................................258
3.4 Library of Functions; Piecewise-defined Functions .............................................................275
3.5 Graphing Techniques: Transformations................................................................................287
3.6 Mathematical Models: Building Functions ...........................................................................305
Chapter Review .............................................................................................................................313
Chapter Test ...................................................................................................................................320
Cumulative Review .......................................................................................................................323
ES
Chapter Projects.............................................................................................................................327
Copyright © 2021 Pearson Education, Inc.
, Chapter 4 Linear and Quadratic Functions
4.1 Properties of Linear Functions and Linear Models ...............................................................329
4.2 Building Linear Models from Data .......................................................................................340
M
4.3 Quadratic Functions and Their Properties ............................................................................346
4.4 Building Quadratic Models from Verbal Descriptions and from Data .................................370
4.5 Inequalities Involving Quadratic Functions ..........................................................................378
Chapter Review .............................................................................................................................397
PR
Chapter Test ...................................................................................................................................405
Cumulative Review .......................................................................................................................408
Chapter Projects .............................................................................................................................411
Chapter 5 Polynomial and Rational Functions
5.1 Polynomial Functions ...........................................................................................................414
5.2 The Graph of a Polynomial Function; Models......................................................................425
ES
5.3 The Real Zeros of a Polynomial Function ............................................................................445
5.4 Complex Zeros; Fundamental Theorem of Algebra .............................................................482
5.5 Properties of Rational Functions ...........................................................................................491
5.6 The Graph of a Rational Function.........................................................................................501
5.7 Polynomial and Rational Inequalities ...................................................................................557
Chapter Review .............................................................................................................................579
Chapter Test ...................................................................................................................................593
SI
Cumulative Review .......................................................................................................................597
Chapter Projects .............................................................................................................................602
Chapter 6 Exponential and Logarithmic Functions
VE
6.1 Composite Functions.............................................................................................................603
6.2 One-to-One Functions; Inverse Functions ............................................................................621
6.3 Exponential Functions...........................................................................................................644
6.4 Logarithmic Functions ..........................................................................................................665
6.5 Properties of Logarithms .......................................................................................................687
6.6 Logarithmic and Exponential Equations ...............................................................................696
6.7 Financial Models ...................................................................................................................717
G
6.8 Exponential Growth and Decay Models; Newton’s Law; Logistic Growth
and Decay Models .................................................................................................................725
6.9 Building Exponential, Logarithmic, and Logistic Models from Data ..................................736
Chapter Review .............................................................................................................................741
R
Chapter Test ...................................................................................................................................753
Cumulative Review .......................................................................................................................757
Chapter Projects .............................................................................................................................760
AD
ES
Copyright © 2021 Pearson Education, Inc.
M
MANUAL
PR
TIM BRITT
Jackson State Community College
ES
COLLEGE ALGEBRA
E NHANCED WITH G RAPHING U TILITIES
SI
EIGHTH EDITION
VE
Michael Sullivan
Chicago State University
G
Michael Sullivan III
Joliet Junior College
R
AD
ES
,M
PR
ES
Please contact https://support.pearson.com/getsupport/s/contactsupport with any queries on this content.
The author and publisher of this book have used their best efforts in preparing this book. These efforts include
the development, research, and testing of the theories and programs to determine their effectiveness. The author
SI
and publisher make no warranty of any kind, expressed or implied, with regard to these programs or the
documentation contained in this book. The author and publisher shall not be liable in any event for incidental or
consequential damages in connection with, or arising out of, the furnishing, performance, or use of these
programs.
VE
Reproduced by Pearson from electronic files supplied by the author.
Copyright © 2021, 2017, 2013 Pearson Education, Inc.
Publishing as Pearson, 21 River Street, Hoboken, NJ 07030. All rights reserved
All rights reserved. Manufactured in the United States of America. This publication is protected by copyright,
G
and permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval
system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or
otherwise. For information regarding permissions, request forms, and the appropriate contacts within the
Pearson Education Global Rights and Permissions department, please visit www.pearsoned.com/permissions/.
R
AD
ISBN-13: 978-0-13-581186-3
ISBN-10: 0-13-581186-4
ES
, Table of Contents
Chapter R Review
M
R.1 Real Numbers ............................................................................................................................1
R.2 Algebra Essentials .....................................................................................................................5
R.3 Geometry Essentials ................................................................................................................11
R.4 Polynomials .............................................................................................................................16
PR
R.5 Factoring Polynomials ............................................................................................................23
R.6 Synthetic Division ...................................................................................................................28
R.7 Rational Expressions ...............................................................................................................30
R.8 nth Roots; Rational Exponents ................................................................................................40
Chapter 1 Graphs, Equations, and Inequalities
ES
1.1 Graphing Utilities; Introduction to Graphing Equations.........................................................50
1.2 Solving Equations Using a Graphing Utility; Linear and Rational Equations .......................57
1.3 Quadratic Equations ................................................................................................................71
1.4 Complex Numbers; Quadratic Equations in the Complex Number System ...........................90
1.5 Radical Equations; Equations Quadratic in Form; Absolute Value Equations;
Factorable Equations ...............................................................................................................96
1.6 Problem Solving: Interest, Mixture, Uniform Motion, Constant Rate Job Applications......117
SI
1.7 Solving Inequalities...............................................................................................................125
Chapter Review .............................................................................................................................137
Chapter Test...................................................................................................................................147
Chapter Projects .............................................................................................................................151
VE
Chapter 2 Graphs
2.1 The Distance and Midpoint Formulas ...................................................................................152
2.2 Intercepts; Symmetry; Graphing Key Equations ..................................................................165
2.3 Lines ......................................................................................................................................182
2.4 Circles ...................................................................................................................................200
2.5 Variation................................................................................................................................215
Chapter Review .............................................................................................................................220
G
Chapter Test ...................................................................................................................................226
Cumulative Review .......................................................................................................................228
Chapter Projects .............................................................................................................................230
R
Chapter 3 Functions and Their Graphs
3.1 Functions ...............................................................................................................................231
3.2 The Graph of a Function .......................................................................................................249
AD
3.3 Properties of Functions .........................................................................................................258
3.4 Library of Functions; Piecewise-defined Functions .............................................................275
3.5 Graphing Techniques: Transformations................................................................................287
3.6 Mathematical Models: Building Functions ...........................................................................305
Chapter Review .............................................................................................................................313
Chapter Test ...................................................................................................................................320
Cumulative Review .......................................................................................................................323
ES
Chapter Projects.............................................................................................................................327
Copyright © 2021 Pearson Education, Inc.
, Chapter 4 Linear and Quadratic Functions
4.1 Properties of Linear Functions and Linear Models ...............................................................329
4.2 Building Linear Models from Data .......................................................................................340
M
4.3 Quadratic Functions and Their Properties ............................................................................346
4.4 Building Quadratic Models from Verbal Descriptions and from Data .................................370
4.5 Inequalities Involving Quadratic Functions ..........................................................................378
Chapter Review .............................................................................................................................397
PR
Chapter Test ...................................................................................................................................405
Cumulative Review .......................................................................................................................408
Chapter Projects .............................................................................................................................411
Chapter 5 Polynomial and Rational Functions
5.1 Polynomial Functions ...........................................................................................................414
5.2 The Graph of a Polynomial Function; Models......................................................................425
ES
5.3 The Real Zeros of a Polynomial Function ............................................................................445
5.4 Complex Zeros; Fundamental Theorem of Algebra .............................................................482
5.5 Properties of Rational Functions ...........................................................................................491
5.6 The Graph of a Rational Function.........................................................................................501
5.7 Polynomial and Rational Inequalities ...................................................................................557
Chapter Review .............................................................................................................................579
Chapter Test ...................................................................................................................................593
SI
Cumulative Review .......................................................................................................................597
Chapter Projects .............................................................................................................................602
Chapter 6 Exponential and Logarithmic Functions
VE
6.1 Composite Functions.............................................................................................................603
6.2 One-to-One Functions; Inverse Functions ............................................................................621
6.3 Exponential Functions...........................................................................................................644
6.4 Logarithmic Functions ..........................................................................................................665
6.5 Properties of Logarithms .......................................................................................................687
6.6 Logarithmic and Exponential Equations ...............................................................................696
6.7 Financial Models ...................................................................................................................717
G
6.8 Exponential Growth and Decay Models; Newton’s Law; Logistic Growth
and Decay Models .................................................................................................................725
6.9 Building Exponential, Logarithmic, and Logistic Models from Data ..................................736
Chapter Review .............................................................................................................................741
R
Chapter Test ...................................................................................................................................753
Cumulative Review .......................................................................................................................757
Chapter Projects .............................................................................................................................760
AD
ES
Copyright © 2021 Pearson Education, Inc.
