INSTRUCTOR’S SOLUTIONS
M
MANUAL
PR
TIM BRITT
Jackson State Community College
ES
COLLEGE ALGEBRA
E LEVENTH E DITION
SI
VE
Michael Sullivan
Chicago State University
G
R
AD
ES
,M
PR
ES
The author and publisher of this book have used their best efforts in preparing this book. These efforts include the
development, research, and testing of the theories and programs to determine their effectiveness. The author and
publisher make no warranty of any kind, expressed or implied, with regard to these programs or the documentation
contained in this book. The author and publisher shall not be liable in any event for incidental or consequential damages
SI
in connection with, or arising out of, the furnishing, performance, or use of these programs.
Reproduced by Pearson from electronic files supplied by the author.
Copyright © 2020, 2016, 2012 Pearson Education, Inc.
VE
Publishing as Pearson, 21 River Street, Hoboken, NJ 07030. All rights reserved
All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any
form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without the prior written
permission of the publisher.
G
R
AD
ES
ISBN-13: 978-0-13-516372-6
ISBN-10: 0-13-516372-2
, Table of Contents
M
Chapter R Review
R.1 Real Numbers ........................................................................................................................... 1
R.2 Algebra Essentials .................................................................................................................... 5
PR
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 Equations and Inequalities
ES
1.1 Linear Equations ..................................................................................................................... 50
1.2 Quadratic Equations ................................................................................................................ 68
1.3 Complex Numbers; Quadratic Equations in the Complex Number System............................ 87
1.4 Radical Equations; Equations Quadratic in Form; Factorable Equations ............................... 93
1.5 Solving Inequalities ............................................................................................................... 116
1.6 Equations and Inequalities Involving Absolute Value .......................................................... 127
SI
1.7 Problem Solving: Interest, Mixture, Uniform Motion, and Constant Rate Job Applications 137
Chapter Review ............................................................................................................................ 145
Chapter Test ................................................................................................................................. 154
Chapter Projects ........................................................................................................................... 156
VE
Chapter 2 Graphs
2.1 The Distance and Midpoint Formulas ................................................................................... 157
2.2 Graphs of Equations in Two Variables; Intercepts; Symmetry ............................................. 170
2.3 Lines ...................................................................................................................................... 184
2.4 Circles ................................................................................................................................... 202
2.5 Variation................................................................................................................................ 216
Chapter Review ............................................................................................................................ 222
G
Chapter Test ................................................................................................................................. 228
Cumulative Review ...................................................................................................................... 230
Chapter Project ............................................................................................................................. 232
R
Chapter 3 Functions and Their Graphs
3.1 Functions ............................................................................................................................... 233
3.2 The Graph of a Function ....................................................................................................... 251
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3.3 Properties of Functions.......................................................................................................... 260
3.4 Library of Functions; Piecewise-defined Functions .............................................................. 277
3.5 Graphing Techniques: Transformations ................................................................................ 289
3.6 Mathematical Models: Building Functions ........................................................................... 307
Chapter Review ............................................................................................................................ 315
Chapter Test ................................................................................................................................. 322
Cumulative Review ...................................................................................................................... 325
Chapter Projects ........................................................................................................................... 329
ES
, Chapter 4 Linear and Quadratic Functions
4.1 Properties of Linear Functions and Linear Models ............................................................... 331
M
4.2 Building Linear Functions from Data ................................................................................... 342
4.3 Quadratic Functions and Their Properties ............................................................................. 348
4.4 Build Quadratic Models from Verbal Descriptions and from Data ...................................... 371
4.5 Inequalities Involving Quadratic Functions .......................................................................... 379
PR
Chapter Review ............................................................................................................................ 399
Chapter Test ................................................................................................................................. 407
Cumulative Review ...................................................................................................................... 409
Chapter Projects ........................................................................................................................... 412
Chapter 5 Polynomial and Rational Functions
5.1 Polynomial Functions............................................................................................................ 415
ES
5.2 Graphing Polynomial Functions; Models.............................................................................. 425
5.3 Properties of Rational Functions ........................................................................................... 441
5.4 The Graph of a Rational Function ......................................................................................... 451
5.5 Polynomial and Rational Inequalities.................................................................................... 507
5.6 The Real Zeros of a Polynomial Function............................................................................. 528
5.7 Complex Zeros; Fundamental Theorem of Algebra .............................................................. 559
Chapter Review ............................................................................................................................ 568
SI
Chapter Test ................................................................................................................................. 583
Cumulative Review ...................................................................................................................... 587
Chapter Projects ........................................................................................................................... 592
Chapter 6 Exponential and Logarithmic Functions
VE
6.1 Composite Functions ............................................................................................................. 594
6.2 One-to-One Functions; Inverse Functions ............................................................................ 612
6.3 Exponential Functions ........................................................................................................... 634
6.4 Logarithmic Functions .......................................................................................................... 655
6.5 Properties of Logarithms ....................................................................................................... 677
6.6 Logarithmic and Exponential Equations ............................................................................... 686
6.7 Financial Models ................................................................................................................... 706
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6.8 Exponential Growth and Decay Models; Newton’s Law; Logistic Growth
and Decay Models .............................................................................................................. 714
6.9 Building Exponential, Logarithmic, and Logistic Models from Data ................................... 723
Chapter Review ............................................................................................................................ 729
R
Chapter Test ................................................................................................................................. 741
Cumulative Review ...................................................................................................................... 745
Chapter Projects ........................................................................................................................... 748
AD
ES
M
MANUAL
PR
TIM BRITT
Jackson State Community College
ES
COLLEGE ALGEBRA
E LEVENTH E DITION
SI
VE
Michael Sullivan
Chicago State University
G
R
AD
ES
,M
PR
ES
The author and publisher of this book have used their best efforts in preparing this book. These efforts include the
development, research, and testing of the theories and programs to determine their effectiveness. The author and
publisher make no warranty of any kind, expressed or implied, with regard to these programs or the documentation
contained in this book. The author and publisher shall not be liable in any event for incidental or consequential damages
SI
in connection with, or arising out of, the furnishing, performance, or use of these programs.
Reproduced by Pearson from electronic files supplied by the author.
Copyright © 2020, 2016, 2012 Pearson Education, Inc.
VE
Publishing as Pearson, 21 River Street, Hoboken, NJ 07030. All rights reserved
All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any
form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without the prior written
permission of the publisher.
G
R
AD
ES
ISBN-13: 978-0-13-516372-6
ISBN-10: 0-13-516372-2
, Table of Contents
M
Chapter R Review
R.1 Real Numbers ........................................................................................................................... 1
R.2 Algebra Essentials .................................................................................................................... 5
PR
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 Equations and Inequalities
ES
1.1 Linear Equations ..................................................................................................................... 50
1.2 Quadratic Equations ................................................................................................................ 68
1.3 Complex Numbers; Quadratic Equations in the Complex Number System............................ 87
1.4 Radical Equations; Equations Quadratic in Form; Factorable Equations ............................... 93
1.5 Solving Inequalities ............................................................................................................... 116
1.6 Equations and Inequalities Involving Absolute Value .......................................................... 127
SI
1.7 Problem Solving: Interest, Mixture, Uniform Motion, and Constant Rate Job Applications 137
Chapter Review ............................................................................................................................ 145
Chapter Test ................................................................................................................................. 154
Chapter Projects ........................................................................................................................... 156
VE
Chapter 2 Graphs
2.1 The Distance and Midpoint Formulas ................................................................................... 157
2.2 Graphs of Equations in Two Variables; Intercepts; Symmetry ............................................. 170
2.3 Lines ...................................................................................................................................... 184
2.4 Circles ................................................................................................................................... 202
2.5 Variation................................................................................................................................ 216
Chapter Review ............................................................................................................................ 222
G
Chapter Test ................................................................................................................................. 228
Cumulative Review ...................................................................................................................... 230
Chapter Project ............................................................................................................................. 232
R
Chapter 3 Functions and Their Graphs
3.1 Functions ............................................................................................................................... 233
3.2 The Graph of a Function ....................................................................................................... 251
AD
3.3 Properties of Functions.......................................................................................................... 260
3.4 Library of Functions; Piecewise-defined Functions .............................................................. 277
3.5 Graphing Techniques: Transformations ................................................................................ 289
3.6 Mathematical Models: Building Functions ........................................................................... 307
Chapter Review ............................................................................................................................ 315
Chapter Test ................................................................................................................................. 322
Cumulative Review ...................................................................................................................... 325
Chapter Projects ........................................................................................................................... 329
ES
, Chapter 4 Linear and Quadratic Functions
4.1 Properties of Linear Functions and Linear Models ............................................................... 331
M
4.2 Building Linear Functions from Data ................................................................................... 342
4.3 Quadratic Functions and Their Properties ............................................................................. 348
4.4 Build Quadratic Models from Verbal Descriptions and from Data ...................................... 371
4.5 Inequalities Involving Quadratic Functions .......................................................................... 379
PR
Chapter Review ............................................................................................................................ 399
Chapter Test ................................................................................................................................. 407
Cumulative Review ...................................................................................................................... 409
Chapter Projects ........................................................................................................................... 412
Chapter 5 Polynomial and Rational Functions
5.1 Polynomial Functions............................................................................................................ 415
ES
5.2 Graphing Polynomial Functions; Models.............................................................................. 425
5.3 Properties of Rational Functions ........................................................................................... 441
5.4 The Graph of a Rational Function ......................................................................................... 451
5.5 Polynomial and Rational Inequalities.................................................................................... 507
5.6 The Real Zeros of a Polynomial Function............................................................................. 528
5.7 Complex Zeros; Fundamental Theorem of Algebra .............................................................. 559
Chapter Review ............................................................................................................................ 568
SI
Chapter Test ................................................................................................................................. 583
Cumulative Review ...................................................................................................................... 587
Chapter Projects ........................................................................................................................... 592
Chapter 6 Exponential and Logarithmic Functions
VE
6.1 Composite Functions ............................................................................................................. 594
6.2 One-to-One Functions; Inverse Functions ............................................................................ 612
6.3 Exponential Functions ........................................................................................................... 634
6.4 Logarithmic Functions .......................................................................................................... 655
6.5 Properties of Logarithms ....................................................................................................... 677
6.6 Logarithmic and Exponential Equations ............................................................................... 686
6.7 Financial Models ................................................................................................................... 706
G
6.8 Exponential Growth and Decay Models; Newton’s Law; Logistic Growth
and Decay Models .............................................................................................................. 714
6.9 Building Exponential, Logarithmic, and Logistic Models from Data ................................... 723
Chapter Review ............................................................................................................................ 729
R
Chapter Test ................................................................................................................................. 741
Cumulative Review ...................................................................................................................... 745
Chapter Projects ........................................................................................................................... 748
AD
ES
