,SOLUTION MANUAL Precalculus Enhanced with
Graphing Utilities, 9th edition Sullivan
Notes
1- The file is chapter after chapter.
2- We have shown you few pages sample.
3- The file contains all Appendix and Excel sheet
if it exists.
4- We have all what you need, we make update
at every time. There are many new editions
waiting you.
5- If you think you purchased the wrong file You
can contact us at every time, we can replace it
with true one.
Our email:
, 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.
,Chapter 8 Applications of Trigonometric Functions
8.1 Right Triangle Trigonometry; Applications......................................................................... 859
8.2 The Law of Sines ................................................................................................................. 873
8.3 The Law of Cosines ............................................................................................................. 887
8.4 Area of a Triangle ................................................................................................................ 900
8.5 Simple Harmonic Motion; Damped Motion; Combining Waves ........................................ 909
Chapter Review ............................................................................................................................ 919
Chapter Test .................................................................................................................................. 926
Cumulative Review ...................................................................................................................... 929
Chapter Projects ............................................................................................................................ 935
Chapter 9 Polar Coordinates; Vectors
9.1 Polar Coordinates ................................................................................................................. 937
9.2 Polar Equations and Graphs ................................................................................................. 946
9.3 The Complex Plane; De Moivre’s Theorem ........................................................................ 975
9.4 Vectors ................................................................................................................................. 988
9.5 The Dot Product ................................................................................................................. 1001
9.6 Vectors in Space ................................................................................................................. 1007
9.7 The Cross Product .............................................................................................................. 1014
Chapter Review .......................................................................................................................... 1025
Chapter Test ................................................................................................................................ 1035
Cumulative Review .................................................................................................................... 1038
Chapter Project ........................................................................................................................... 1041
Chapter 10 Analytic Geometry
10.2 The Parabola....................................................................................................................... 1042
10.3 The Ellipse ......................................................................................................................... 1058
10.4 The Hyperbola .................................................................................................................... 1075
10.5 Rotation of Axes; General Form of a Conic ...................................................................... 1095
10.6 Polar Equations of Conics .................................................................................................. 1108
10.7 Plane Curves and Parametric Equations ............................................................................ 1117
Chapter Review .......................................................................................................................... 1132
Chapter Test ................................................................................................................................ 1142
Cumulative Review .................................................................................................................... 1146
Chapter Project ........................................................................................................................... 1149
Chapter 11 Systems of Equations and Inequalities
11.1 Systems of Linear Equations: Substitution and Elimination.............................................. 1150
11.2 Systems of Linear Equations: Matrices.............................................................................. 1173
11.3 Systems of Linear Equations: Determinants ...................................................................... 1197
11.4 Matrix Algebra ................................................................................................................... 1211
11.5 Partial Fraction Decomposition.......................................................................................... 1228
11.6 Systems of Nonlinear Equations ........................................................................................ 1246
11.7 Systems of Inequalities ...................................................................................................... 1274
11.8 Linear Programming .......................................................................................................... 1290
Chapter Review .......................................................................................................................... 1303
Chapter Test ................................................................................................................................ 1318
Cumulative Review .................................................................................................................... 1326
Chapter Project ........................................................................................................................... 1330
Copyright © 2026 Pearson Education, Inc.
,Chapter 12 Sequences; Induction; the Binomial Theorem
12.1 Sequences ........................................................................................................................... 1331
12.2 Arithmetic Sequences......................................................................................................... 1345
12.3 Geometric Sequences; Geometric Series ........................................................................... 1354
12.4 The Limit of a Sequence; Infinite Series............................................................................ 1365
12.5 Mathematical Induction ..................................................................................................... 1370
12.6 The Binomial Theorem ...................................................................................................... 1379
Chapter Review .......................................................................................................................... 1386
Chapter Test ................................................................................................................................ 1391
Cumulative Review .................................................................................................................... 1394
Chapter Project ........................................................................................................................... 1397
Chapter 13 Counting and Probability
13.1 Counting ............................................................................................................................. 1398
13.2 Permutations and Combinations ........................................................................................ 1401
13.3 Probability .......................................................................................................................... 1406
Chapter Review .......................................................................................................................... 1413
Chapter Test ................................................................................................................................ 1415
Cumulative Review .................................................................................................................... 1416
Chapter Project ........................................................................................................................... 1419
Chapter 14 A Preview of Calculus: The Limit, Derivative, and Integral of a Function
14.1 Investigating Limits Using Tables and Graphs .................................................................. 1421
14.2 Algebraic Techniques for Finding Limits .......................................................................... 1427
14.3 One-sided Limits; Continuity ............................................................................................. 1431
14.4 The Tangent Problem; The Derivative ............................................................................... 1439
14.5 The Area Problem; The Integral ........................................................................................ 1449
Chapter Review .......................................................................................................................... 1463
Chapter Test ................................................................................................................................ 1470
Chapter Project ........................................................................................................................... 1473
Appendix A: Review
A.1 Algebra Essentials .............................................................................................................. 1476
A.2 Geometry Essentials ........................................................................................................... 1482
A.3 Polynomials ........................................................................................................................ 1487
A.4 Synthetic Division .............................................................................................................. 1496
A.5 Rational Expressions .......................................................................................................... 1498
A.6 Solving Equations .............................................................................................................. 1503
A.7 Complex Numbers; Quadratic Equations in the Complex Number System ...................... 1519
A.8 Problem Solving: Interest, Mixture, Uniform Motion, Constant Rate Job Applications ... 1524
A.9 Interval Notation; Solving Inequalities .............................................................................. 1532
A.10 nth Roots; Rational Exponents ........................................................................................... 1544
Copyright © 2026 Pearson Education, Inc.
, Chapter 1
Graphs
Section 1.1 (f) x-axis
1. 0
2.
3. x-coordinate; y-coordinate; quadrants
4. False; points that lie in Quadrant IV will have a
positive x-coordinate and a negative y-coordinate.
The point 1, 4 lies in Quadrant II.
9. The points will be on a vertical line that is two
units to the right of the y-axis.
5. d
6. c
7. (a) Quadrant II
(b) x-axis
(c) Quadrant III
(d) Quadrant I
(e) y-axis
(f) Quadrant IV
10. The points will be on a horizontal line that is
three units above the x-axis.
8. (a) Quadrant I
(b) Quadrant III
(c) Quadrant II
(d) Quadrant I
(e) y-axis
11. 1, 4 ; Quadrant II
12. (3, 4); Quadrant I
13. (3, 1); Quadrant I
1
Copyright © 2026 Pearson Education, Inc.
, Chapter 1: Graphs
14. 6, 4 ; Quadrant III 21. X min 6
X max 6
15. X min 11 X scl 2
X max 5 Y min 4
X scl 1 Y max 4
Y min 3 Y scl 2
Y max 6
Y scl 1 22. X min 3
X max 3
16. X min 3 X scl 1
X max 7 Y min 2
X scl 1 Y max 2
Y min 4 Y scl 1
Y max 9
Y scl 1 23. X min 6
X max 6
17. X min 30 X scl 2
X max 50 Y min 1
X scl 10 Y max 3
Y min 90
Y scl 1
Y max 50
Y scl 10 24. X min 9
X max 9
18. X min 90
X scl 3
X max 30
Y min 12
X scl 10
Y max 4
Y min 50
Y scl 4
Y max 70
Y scl 10 25. X min 3
X max 9
19. X min 10
X scl 1
X max 110
Y min 2
X scl 10
Y max 10
Y min 10
Y scl 2
Y max 160
Y scl 10 26. X min 22
X max 10
20. X min 20
X scl 2
X max 110
Y min 4
X scl 10
Y max 8
Y min 10
Y scl 1
Y max 60
Y scl 10
2
Copyright © 2026 Pearson Education, Inc.
Graphing Utilities, 9th edition Sullivan
Notes
1- The file is chapter after chapter.
2- We have shown you few pages sample.
3- The file contains all Appendix and Excel sheet
if it exists.
4- We have all what you need, we make update
at every time. There are many new editions
waiting you.
5- If you think you purchased the wrong file You
can contact us at every time, we can replace it
with true one.
Our email:
, 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.
,Chapter 8 Applications of Trigonometric Functions
8.1 Right Triangle Trigonometry; Applications......................................................................... 859
8.2 The Law of Sines ................................................................................................................. 873
8.3 The Law of Cosines ............................................................................................................. 887
8.4 Area of a Triangle ................................................................................................................ 900
8.5 Simple Harmonic Motion; Damped Motion; Combining Waves ........................................ 909
Chapter Review ............................................................................................................................ 919
Chapter Test .................................................................................................................................. 926
Cumulative Review ...................................................................................................................... 929
Chapter Projects ............................................................................................................................ 935
Chapter 9 Polar Coordinates; Vectors
9.1 Polar Coordinates ................................................................................................................. 937
9.2 Polar Equations and Graphs ................................................................................................. 946
9.3 The Complex Plane; De Moivre’s Theorem ........................................................................ 975
9.4 Vectors ................................................................................................................................. 988
9.5 The Dot Product ................................................................................................................. 1001
9.6 Vectors in Space ................................................................................................................. 1007
9.7 The Cross Product .............................................................................................................. 1014
Chapter Review .......................................................................................................................... 1025
Chapter Test ................................................................................................................................ 1035
Cumulative Review .................................................................................................................... 1038
Chapter Project ........................................................................................................................... 1041
Chapter 10 Analytic Geometry
10.2 The Parabola....................................................................................................................... 1042
10.3 The Ellipse ......................................................................................................................... 1058
10.4 The Hyperbola .................................................................................................................... 1075
10.5 Rotation of Axes; General Form of a Conic ...................................................................... 1095
10.6 Polar Equations of Conics .................................................................................................. 1108
10.7 Plane Curves and Parametric Equations ............................................................................ 1117
Chapter Review .......................................................................................................................... 1132
Chapter Test ................................................................................................................................ 1142
Cumulative Review .................................................................................................................... 1146
Chapter Project ........................................................................................................................... 1149
Chapter 11 Systems of Equations and Inequalities
11.1 Systems of Linear Equations: Substitution and Elimination.............................................. 1150
11.2 Systems of Linear Equations: Matrices.............................................................................. 1173
11.3 Systems of Linear Equations: Determinants ...................................................................... 1197
11.4 Matrix Algebra ................................................................................................................... 1211
11.5 Partial Fraction Decomposition.......................................................................................... 1228
11.6 Systems of Nonlinear Equations ........................................................................................ 1246
11.7 Systems of Inequalities ...................................................................................................... 1274
11.8 Linear Programming .......................................................................................................... 1290
Chapter Review .......................................................................................................................... 1303
Chapter Test ................................................................................................................................ 1318
Cumulative Review .................................................................................................................... 1326
Chapter Project ........................................................................................................................... 1330
Copyright © 2026 Pearson Education, Inc.
,Chapter 12 Sequences; Induction; the Binomial Theorem
12.1 Sequences ........................................................................................................................... 1331
12.2 Arithmetic Sequences......................................................................................................... 1345
12.3 Geometric Sequences; Geometric Series ........................................................................... 1354
12.4 The Limit of a Sequence; Infinite Series............................................................................ 1365
12.5 Mathematical Induction ..................................................................................................... 1370
12.6 The Binomial Theorem ...................................................................................................... 1379
Chapter Review .......................................................................................................................... 1386
Chapter Test ................................................................................................................................ 1391
Cumulative Review .................................................................................................................... 1394
Chapter Project ........................................................................................................................... 1397
Chapter 13 Counting and Probability
13.1 Counting ............................................................................................................................. 1398
13.2 Permutations and Combinations ........................................................................................ 1401
13.3 Probability .......................................................................................................................... 1406
Chapter Review .......................................................................................................................... 1413
Chapter Test ................................................................................................................................ 1415
Cumulative Review .................................................................................................................... 1416
Chapter Project ........................................................................................................................... 1419
Chapter 14 A Preview of Calculus: The Limit, Derivative, and Integral of a Function
14.1 Investigating Limits Using Tables and Graphs .................................................................. 1421
14.2 Algebraic Techniques for Finding Limits .......................................................................... 1427
14.3 One-sided Limits; Continuity ............................................................................................. 1431
14.4 The Tangent Problem; The Derivative ............................................................................... 1439
14.5 The Area Problem; The Integral ........................................................................................ 1449
Chapter Review .......................................................................................................................... 1463
Chapter Test ................................................................................................................................ 1470
Chapter Project ........................................................................................................................... 1473
Appendix A: Review
A.1 Algebra Essentials .............................................................................................................. 1476
A.2 Geometry Essentials ........................................................................................................... 1482
A.3 Polynomials ........................................................................................................................ 1487
A.4 Synthetic Division .............................................................................................................. 1496
A.5 Rational Expressions .......................................................................................................... 1498
A.6 Solving Equations .............................................................................................................. 1503
A.7 Complex Numbers; Quadratic Equations in the Complex Number System ...................... 1519
A.8 Problem Solving: Interest, Mixture, Uniform Motion, Constant Rate Job Applications ... 1524
A.9 Interval Notation; Solving Inequalities .............................................................................. 1532
A.10 nth Roots; Rational Exponents ........................................................................................... 1544
Copyright © 2026 Pearson Education, Inc.
, Chapter 1
Graphs
Section 1.1 (f) x-axis
1. 0
2.
3. x-coordinate; y-coordinate; quadrants
4. False; points that lie in Quadrant IV will have a
positive x-coordinate and a negative y-coordinate.
The point 1, 4 lies in Quadrant II.
9. The points will be on a vertical line that is two
units to the right of the y-axis.
5. d
6. c
7. (a) Quadrant II
(b) x-axis
(c) Quadrant III
(d) Quadrant I
(e) y-axis
(f) Quadrant IV
10. The points will be on a horizontal line that is
three units above the x-axis.
8. (a) Quadrant I
(b) Quadrant III
(c) Quadrant II
(d) Quadrant I
(e) y-axis
11. 1, 4 ; Quadrant II
12. (3, 4); Quadrant I
13. (3, 1); Quadrant I
1
Copyright © 2026 Pearson Education, Inc.
, Chapter 1: Graphs
14. 6, 4 ; Quadrant III 21. X min 6
X max 6
15. X min 11 X scl 2
X max 5 Y min 4
X scl 1 Y max 4
Y min 3 Y scl 2
Y max 6
Y scl 1 22. X min 3
X max 3
16. X min 3 X scl 1
X max 7 Y min 2
X scl 1 Y max 2
Y min 4 Y scl 1
Y max 9
Y scl 1 23. X min 6
X max 6
17. X min 30 X scl 2
X max 50 Y min 1
X scl 10 Y max 3
Y min 90
Y scl 1
Y max 50
Y scl 10 24. X min 9
X max 9
18. X min 90
X scl 3
X max 30
Y min 12
X scl 10
Y max 4
Y min 50
Y scl 4
Y max 70
Y scl 10 25. X min 3
X max 9
19. X min 10
X scl 1
X max 110
Y min 2
X scl 10
Y max 10
Y min 10
Y scl 2
Y max 160
Y scl 10 26. X min 22
X max 10
20. X min 20
X scl 2
X max 110
Y min 4
X scl 10
Y max 8
Y min 10
Y scl 1
Y max 60
Y scl 10
2
Copyright © 2026 Pearson Education, Inc.
