INSTRUCTOR’S SOLUTIONS
MANUAL
GEX INC.
ALGEBRA & TRIGONOMETRY
ENHANCED WITH GRAPHING
UTILITIES
NINTH EDITION
Michael Sullivan
Chicago State University
Michael Sullivan, III
Joliet Junior College
and
Florida SouthWestern State College
,Copyright © 2026, 2021, 2017 by Pearson Education, Inc. or its affiliates. All Rights Reserved. Manufactured in the
United States of America. This publication is protected by copyright, 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/.
PEARSON and MYLAB are exclusive trademarks owned by Pearson Education, Inc. or its affiliates in the U.S.
and/or other countries.
Unless otherwise indicated herein, any third-party trademarks, logos, or icons that may appear in this work are the
property of their respective owners, and any references to third-party trademarks, logos, icons, or other trade dress are
for demonstrative or descriptive purposes only. Such references are not intended to imply any sponsorship,
endorsement, authorization, or promotion of Pearson’s products by the owners of such marks, or any relationship
between the owner and Pearson Education, Inc., or its affiliates, authors, licensees, or distributors.
PPID: A103000398499
, Table of Contents
Chapter R Review
R.1 Real Numbers .......................................................................................................................... 1
R.2 Algebra Essentials ................................................................................................................... 5
R.3 Geometry Essentials .............................................................................................................. 11
R.4 Polynomials ........................................................................................................................... 16
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
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 .......................... 89
1.5 Radical Equations; Equations Quadratic in Form; Absolute Value Equations;
Factorable Equations ............................................................................................................. 95
1.6 Problem Solving: Interest, Mixture, Uniform Motion, Constant Rate
Job Applications .................................................................................................................. 115
1.7 Solving Inequalities ............................................................................................................. 123
Chapter Review ............................................................................................................................ 134
Chapter Test ................................................................................................................................. 144
Chapter Project ............................................................................................................................. 149
Chapter 2 Graphs
2.1 The Distance and Midpoint Formulas ................................................................................. 150
2.2 Intercepts; Symmetry; Graphing Key Equations ................................................................. 162
2.3 Lines .................................................................................................................................... 178
2.4 Circles .................................................................................................................................. 195
2.5 Variation .............................................................................................................................. 208
Chapter Review ............................................................................................................................ 214
Chapter Test ................................................................................................................................. 220
Cumulative Review ...................................................................................................................... 221
Chapter Project ............................................................................................................................. 224
Chapter 3 Functions and Their Graphs
3.1 Functions ............................................................................................................................. 225
3.2 The Graph of a Function ...................................................................................................... 243
3.3 Properties of Functions ........................................................................................................ 252
3.4 Library of Functions; Piecewise-defined Functions ............................................................ 269
3.5 Graphing Techniques: Transformations .............................................................................. 282
3.6 Mathematical Models: Building Functions.......................................................................... 300
Chapter Review ............................................................................................................................ 307
Chapter Test ................................................................................................................................. 314
Cumulative Review ...................................................................................................................... 318
Chapter Projects ........................................................................................................................... 321
Copyright © 2026 Pearson Education, Inc.
, Chapter 4 Linear and Quadratic Functions
4.1 Properties of Linear Functions and Linear Models.............................................................. 322
4.2 Building Linear Models from Data ...................................................................................... 333
4.3 Quadratic Functions and Their Properties ........................................................................... 339
4.4 Build Quadratic Models from Verbal Descriptions and from Data ..................................... 363
4.5 Inequalities Involving Quadratic Functions ......................................................................... 371
Chapter Review ............................................................................................................................ 390
Chapter Test ................................................................................................................................. 398
Cumulative Review ...................................................................................................................... 400
Chapter Project ............................................................................................................................. 403
Chapter 5 Polynomial and Rational Functions
5.1 Polynomial Functions .......................................................................................................... 404
5.2 The Graph of a Polynomial Function; Models .................................................................... 414
5.3 The Real Zeros of a Polynomial Function ........................................................................... 435
5.4 Complex Zeros; Fundamental Theorem of Algebra ............................................................ 472
5.5 Properties of Rational Functions ......................................................................................... 481
5.6 The Graph of a Rational Function ....................................................................................... 491
5.7 Polynomial and Rational Inequalities .................................................................................. 546
Chapter Review ............................................................................................................................ 567
Chapter Test ................................................................................................................................. 582
Cumulative Review ...................................................................................................................... 587
Chapter Project ............................................................................................................................. 591
Chapter 6 Exponential and Logarithmic Functions
6.1 Composite Functions ........................................................................................................... 592
6.2 One-to-One Functions; Inverse Functions ........................................................................... 610
6.3 Exponential Functions ......................................................................................................... 633
6.4 Logarithmic Functions ......................................................................................................... 654
6.5 Properties of Logarithms ..................................................................................................... 676
6.6 Logarithmic and Exponential Equations.............................................................................. 685
6.7 Financial Models ................................................................................................................. 708
6.8 Exponential Growth and Decay Models; Newton’s Law; Logistic Growth
and Decay Models ............................................................................................................... 716
6.9 Building Exponential, Logarithmic, and Logistic Models from Data ................................. 728
Chapter Review ............................................................................................................................ 734
Chapter Test ................................................................................................................................. 746
Cumulative Review ...................................................................................................................... 750
Chapter Project ............................................................................................................................. 753
Copyright © 2026 Pearson Education, Inc.
MANUAL
GEX INC.
ALGEBRA & TRIGONOMETRY
ENHANCED WITH GRAPHING
UTILITIES
NINTH EDITION
Michael Sullivan
Chicago State University
Michael Sullivan, III
Joliet Junior College
and
Florida SouthWestern State College
,Copyright © 2026, 2021, 2017 by Pearson Education, Inc. or its affiliates. All Rights Reserved. Manufactured in the
United States of America. This publication is protected by copyright, 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/.
PEARSON and MYLAB are exclusive trademarks owned by Pearson Education, Inc. or its affiliates in the U.S.
and/or other countries.
Unless otherwise indicated herein, any third-party trademarks, logos, or icons that may appear in this work are the
property of their respective owners, and any references to third-party trademarks, logos, icons, or other trade dress are
for demonstrative or descriptive purposes only. Such references are not intended to imply any sponsorship,
endorsement, authorization, or promotion of Pearson’s products by the owners of such marks, or any relationship
between the owner and Pearson Education, Inc., or its affiliates, authors, licensees, or distributors.
PPID: A103000398499
, Table of Contents
Chapter R Review
R.1 Real Numbers .......................................................................................................................... 1
R.2 Algebra Essentials ................................................................................................................... 5
R.3 Geometry Essentials .............................................................................................................. 11
R.4 Polynomials ........................................................................................................................... 16
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
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 .......................... 89
1.5 Radical Equations; Equations Quadratic in Form; Absolute Value Equations;
Factorable Equations ............................................................................................................. 95
1.6 Problem Solving: Interest, Mixture, Uniform Motion, Constant Rate
Job Applications .................................................................................................................. 115
1.7 Solving Inequalities ............................................................................................................. 123
Chapter Review ............................................................................................................................ 134
Chapter Test ................................................................................................................................. 144
Chapter Project ............................................................................................................................. 149
Chapter 2 Graphs
2.1 The Distance and Midpoint Formulas ................................................................................. 150
2.2 Intercepts; Symmetry; Graphing Key Equations ................................................................. 162
2.3 Lines .................................................................................................................................... 178
2.4 Circles .................................................................................................................................. 195
2.5 Variation .............................................................................................................................. 208
Chapter Review ............................................................................................................................ 214
Chapter Test ................................................................................................................................. 220
Cumulative Review ...................................................................................................................... 221
Chapter Project ............................................................................................................................. 224
Chapter 3 Functions and Their Graphs
3.1 Functions ............................................................................................................................. 225
3.2 The Graph of a Function ...................................................................................................... 243
3.3 Properties of Functions ........................................................................................................ 252
3.4 Library of Functions; Piecewise-defined Functions ............................................................ 269
3.5 Graphing Techniques: Transformations .............................................................................. 282
3.6 Mathematical Models: Building Functions.......................................................................... 300
Chapter Review ............................................................................................................................ 307
Chapter Test ................................................................................................................................. 314
Cumulative Review ...................................................................................................................... 318
Chapter Projects ........................................................................................................................... 321
Copyright © 2026 Pearson Education, Inc.
, Chapter 4 Linear and Quadratic Functions
4.1 Properties of Linear Functions and Linear Models.............................................................. 322
4.2 Building Linear Models from Data ...................................................................................... 333
4.3 Quadratic Functions and Their Properties ........................................................................... 339
4.4 Build Quadratic Models from Verbal Descriptions and from Data ..................................... 363
4.5 Inequalities Involving Quadratic Functions ......................................................................... 371
Chapter Review ............................................................................................................................ 390
Chapter Test ................................................................................................................................. 398
Cumulative Review ...................................................................................................................... 400
Chapter Project ............................................................................................................................. 403
Chapter 5 Polynomial and Rational Functions
5.1 Polynomial Functions .......................................................................................................... 404
5.2 The Graph of a Polynomial Function; Models .................................................................... 414
5.3 The Real Zeros of a Polynomial Function ........................................................................... 435
5.4 Complex Zeros; Fundamental Theorem of Algebra ............................................................ 472
5.5 Properties of Rational Functions ......................................................................................... 481
5.6 The Graph of a Rational Function ....................................................................................... 491
5.7 Polynomial and Rational Inequalities .................................................................................. 546
Chapter Review ............................................................................................................................ 567
Chapter Test ................................................................................................................................. 582
Cumulative Review ...................................................................................................................... 587
Chapter Project ............................................................................................................................. 591
Chapter 6 Exponential and Logarithmic Functions
6.1 Composite Functions ........................................................................................................... 592
6.2 One-to-One Functions; Inverse Functions ........................................................................... 610
6.3 Exponential Functions ......................................................................................................... 633
6.4 Logarithmic Functions ......................................................................................................... 654
6.5 Properties of Logarithms ..................................................................................................... 676
6.6 Logarithmic and Exponential Equations.............................................................................. 685
6.7 Financial Models ................................................................................................................. 708
6.8 Exponential Growth and Decay Models; Newton’s Law; Logistic Growth
and Decay Models ............................................................................................................... 716
6.9 Building Exponential, Logarithmic, and Logistic Models from Data ................................. 728
Chapter Review ............................................................................................................................ 734
Chapter Test ................................................................................................................................. 746
Cumulative Review ...................................................................................................................... 750
Chapter Project ............................................................................................................................. 753
Copyright © 2026 Pearson Education, Inc.
