INSTRUCTOR’S SOLUTIONS
MANUAL
GEX INC.
PRECALCULUS
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: A103000398441
, Table of Contents
Chapter 1 Graphs
1.1 Graphing Utilities; Introduction to Graphing Equations .......................................................... 1
1.2 The Distance and Midpoint Formulas ...................................................................................... 8
1.3 Intercepts; Symmetry; Graphing Key Equations ................................................................... 20
1.4 Solving Equations Using a Graphing Utility ......................................................................... 35
1.5 Lines ....................................................................................................................................... 41
1.6 Circles .................................................................................................................................... 58
Chapter Review .............................................................................................................................. 71
Chapter Test .................................................................................................................................... 78
Chapter Project ............................................................................................................................... 81
Chapter 2 Functions and Their Graphs
2.1 Functions ................................................................................................................................ 82
2.2 The Graph of a Function ...................................................................................................... 100
2.3 Properties of Functions ........................................................................................................ 109
2.4 Library of Functions; Piecewise-defined Functions ............................................................ 126
2.5 Graphing Techniques: Transformations ............................................................................... 138
2.6 Mathematical Models: Building Functions .......................................................................... 156
Chapter Review ............................................................................................................................ 163
Chapter Test .................................................................................................................................. 170
Cumulative Review ...................................................................................................................... 174
Chapter Project ............................................................................................................................. 177
Chapter 3 Linear and Quadratic Functions
3.1 Properties of Linear Functions and Linear Models .............................................................. 178
3.2 Building Linear Models from Data ...................................................................................... 189
3.3 Quadratic Functions and Their Properties............................................................................ 195
3.4 Build Quadratic Models from Verbal Descriptions and from Data ..................................... 219
3.5 Inequalities Involving Quadratic Functions ......................................................................... 226
Chapter Review ............................................................................................................................ 246
Chapter Test .................................................................................................................................. 253
Cumulative Review ...................................................................................................................... 256
Chapter Project ............................................................................................................................. 258
Chapter 4 Polynomial and Rational Functions
4.1 Polynomial Functions........................................................................................................... 259
4.2 The Graph of a Polynomial Function; Models ..................................................................... 270
4.3 The Real Zeros of a Polynomial Function ........................................................................... 290
4.4 Complex Zeros; Fundamental Theorem of Algebra ............................................................ 322
4.5 Properties of Rational Functions .......................................................................................... 331
4.6 The Graph of a Rational Function ........................................................................................ 340
4.7 Polynomial and Rational Inequalities .................................................................................. 395
Chapter Review ............................................................................................................................ 417
Chapter Test .................................................................................................................................. 433
Cumulative Review ...................................................................................................................... 437
Chapter Project ............................................................................................................................. 441
Copyright © 2026 Pearson Education, Inc.
, Chapter 5 Exponential and Logarithmic Functions
5.1 Composite Functions ............................................................................................................ 442
5.2 One-to-One Functions; Inverse Functions ........................................................................... 461
5.3 Exponential Functions .......................................................................................................... 483
5.4 Logarithmic Functions ......................................................................................................... 505
5.5 Properties of Logarithms ...................................................................................................... 527
5.6 Logarithmic and Exponential Equations .............................................................................. 536
5.7 Financial Models .................................................................................................................. 559
5.8 Exponential Growth and Decay Models; Newton’s Law; Logistic Growth
and Decay Models ................................................................................................................ 567
5.9 Building Exponential, Logarithmic, and Logistic Models from Data ................................. 578
Chapter Review ............................................................................................................................ 583
Chapter Test .................................................................................................................................. 595
Cumulative Review ...................................................................................................................... 599
Chapter Project ............................................................................................................................. 602
Chapter 6 Trigonometric Functions
6.1 Angles, Arc length, and Circular Motion ............................................................................. 603
6.2 Trigonometric Functions: Unit Circle Approach ................................................................. 612
6.3 Properties of the Trigonometric Functions .......................................................................... 630
6.4 Graphs of the Sine and Cosine Functions ............................................................................ 644
6.5 Graphs of the Tangent, Cotangent, Cosecant, and Secant Functions ................................... 665
6.6 Phase Shift; Sinusoidal Curve Fitting .................................................................................. 675
Chapter Review ............................................................................................................................ 687
Chapter Test .................................................................................................................................. 695
Cumulative Review ...................................................................................................................... 699
Chapter Project ............................................................................................................................. 703
Chapter 7 Analytic Trigonometry
7.1 The Inverse Sine, Cosine, and Tangent Functions ............................................................... 704
7.2 The Inverse Trigonometric Functions (Continued).............................................................. 718
7.3 Trigonometric Equations ..................................................................................................... 730
7.4 Trigonometric Identities ....................................................................................................... 751
7.5 Sum and Difference Formulas ............................................................................................. 764
7.6 Double-angle and Half-angle Formulas ............................................................................... 790
7.7 Product-to-Sum and Sum-to-Product Formulas ................................................................... 819
Chapter Review ............................................................................................................................ 833
Chapter Test .................................................................................................................................. 848
Cumulative Review ...................................................................................................................... 853
Chapter Project ............................................................................................................................. 858
Copyright © 2026 Pearson Education, Inc.
MANUAL
GEX INC.
PRECALCULUS
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: A103000398441
, Table of Contents
Chapter 1 Graphs
1.1 Graphing Utilities; Introduction to Graphing Equations .......................................................... 1
1.2 The Distance and Midpoint Formulas ...................................................................................... 8
1.3 Intercepts; Symmetry; Graphing Key Equations ................................................................... 20
1.4 Solving Equations Using a Graphing Utility ......................................................................... 35
1.5 Lines ....................................................................................................................................... 41
1.6 Circles .................................................................................................................................... 58
Chapter Review .............................................................................................................................. 71
Chapter Test .................................................................................................................................... 78
Chapter Project ............................................................................................................................... 81
Chapter 2 Functions and Their Graphs
2.1 Functions ................................................................................................................................ 82
2.2 The Graph of a Function ...................................................................................................... 100
2.3 Properties of Functions ........................................................................................................ 109
2.4 Library of Functions; Piecewise-defined Functions ............................................................ 126
2.5 Graphing Techniques: Transformations ............................................................................... 138
2.6 Mathematical Models: Building Functions .......................................................................... 156
Chapter Review ............................................................................................................................ 163
Chapter Test .................................................................................................................................. 170
Cumulative Review ...................................................................................................................... 174
Chapter Project ............................................................................................................................. 177
Chapter 3 Linear and Quadratic Functions
3.1 Properties of Linear Functions and Linear Models .............................................................. 178
3.2 Building Linear Models from Data ...................................................................................... 189
3.3 Quadratic Functions and Their Properties............................................................................ 195
3.4 Build Quadratic Models from Verbal Descriptions and from Data ..................................... 219
3.5 Inequalities Involving Quadratic Functions ......................................................................... 226
Chapter Review ............................................................................................................................ 246
Chapter Test .................................................................................................................................. 253
Cumulative Review ...................................................................................................................... 256
Chapter Project ............................................................................................................................. 258
Chapter 4 Polynomial and Rational Functions
4.1 Polynomial Functions........................................................................................................... 259
4.2 The Graph of a Polynomial Function; Models ..................................................................... 270
4.3 The Real Zeros of a Polynomial Function ........................................................................... 290
4.4 Complex Zeros; Fundamental Theorem of Algebra ............................................................ 322
4.5 Properties of Rational Functions .......................................................................................... 331
4.6 The Graph of a Rational Function ........................................................................................ 340
4.7 Polynomial and Rational Inequalities .................................................................................. 395
Chapter Review ............................................................................................................................ 417
Chapter Test .................................................................................................................................. 433
Cumulative Review ...................................................................................................................... 437
Chapter Project ............................................................................................................................. 441
Copyright © 2026 Pearson Education, Inc.
, Chapter 5 Exponential and Logarithmic Functions
5.1 Composite Functions ............................................................................................................ 442
5.2 One-to-One Functions; Inverse Functions ........................................................................... 461
5.3 Exponential Functions .......................................................................................................... 483
5.4 Logarithmic Functions ......................................................................................................... 505
5.5 Properties of Logarithms ...................................................................................................... 527
5.6 Logarithmic and Exponential Equations .............................................................................. 536
5.7 Financial Models .................................................................................................................. 559
5.8 Exponential Growth and Decay Models; Newton’s Law; Logistic Growth
and Decay Models ................................................................................................................ 567
5.9 Building Exponential, Logarithmic, and Logistic Models from Data ................................. 578
Chapter Review ............................................................................................................................ 583
Chapter Test .................................................................................................................................. 595
Cumulative Review ...................................................................................................................... 599
Chapter Project ............................................................................................................................. 602
Chapter 6 Trigonometric Functions
6.1 Angles, Arc length, and Circular Motion ............................................................................. 603
6.2 Trigonometric Functions: Unit Circle Approach ................................................................. 612
6.3 Properties of the Trigonometric Functions .......................................................................... 630
6.4 Graphs of the Sine and Cosine Functions ............................................................................ 644
6.5 Graphs of the Tangent, Cotangent, Cosecant, and Secant Functions ................................... 665
6.6 Phase Shift; Sinusoidal Curve Fitting .................................................................................. 675
Chapter Review ............................................................................................................................ 687
Chapter Test .................................................................................................................................. 695
Cumulative Review ...................................................................................................................... 699
Chapter Project ............................................................................................................................. 703
Chapter 7 Analytic Trigonometry
7.1 The Inverse Sine, Cosine, and Tangent Functions ............................................................... 704
7.2 The Inverse Trigonometric Functions (Continued).............................................................. 718
7.3 Trigonometric Equations ..................................................................................................... 730
7.4 Trigonometric Identities ....................................................................................................... 751
7.5 Sum and Difference Formulas ............................................................................................. 764
7.6 Double-angle and Half-angle Formulas ............................................................................... 790
7.7 Product-to-Sum and Sum-to-Product Formulas ................................................................... 819
Chapter Review ............................................................................................................................ 833
Chapter Test .................................................................................................................................. 848
Cumulative Review ...................................................................................................................... 853
Chapter Project ............................................................................................................................. 858
Copyright © 2026 Pearson Education, Inc.
