VE
R
INSTRUCTOR’S SOLUTIONS
IF
IE
MANUAL
D
BR
TIM BRITT
Jackson State Community College
AI
N
BO
ALGEBRA AND
O
ST
TRIGONOMETRY
ER
E LEVENTH E DITION
Michael Sullivan
Chicago State University
VERIFIEDBRAINBOOSTER
, VE
R
IF
IE
D
BR
AI
N
BO
The author and publisher of this book have used their best efforts in preparing this book. These efforts include the
O
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
ST
contained in this book. The author and publisher shall not be liable in any event for incidental or consequential damages
in connection with, or arising out of, the furnishing, performance, or use of these programs.
ER
Reproduced by Pearson from electronic files supplied by the author.
Copyright © 2020, 2016, 2012 Pearson Education, Inc.
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.
ISBN-13: 978-0-13-518932-0
ISBN-10: 0-13-518932-2
VERIFIEDBRAINBOOSTER
, VE
R
Table of Contents
IF
IE
Chapter R Review
R.1 Real Numbers ........................................................................................................................... 1
D
R.2 Algebra Essentials .................................................................................................................... 5
R.3 Geometry Essentials ............................................................................................................... 11
BR
R.4 Polynomials ............................................................................................................................ 16
R.5 Factoring Polynomials ............................................................................................................ 23
R.6 Synthetic Division .................................................................................................................. 28
AI
R.7 Rational Expressions .............................................................................................................. 30
R.8 nth Roots; Rational Exponents ............................................................................................... 40
N
Chapter 1 Equations and Inequalities
BO
1.1 Linear Equations ..................................................................................................................... 50
1.2 Quadratic Equations ................................................................................................................ 68
1.3 Complex Numbers; Quadratic Equations in the Complex Number System............................ 87
O
1.4 Radical Equations; Equations Quadratic in Form; Factorable Equations ............................... 93
1.5 Solving Inequalities ............................................................................................................... 116
ST
1.6 Equations and Inequalities Involving Absolute Value .......................................................... 127
1.7 Problem Solving: Interest, Mixture, Uniform Motion, Constant Rate Job Applications ...... 137
Chapter Review ............................................................................................................................ 145
ER
Chapter Test ................................................................................................................................. 154
Chapter Projects ........................................................................................................................... 156
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
Chapter Test ................................................................................................................................. 228
Cumulative Review ...................................................................................................................... 230
Chapter Project ............................................................................................................................. 232
Chapter 3 Functions and Their Graphs
3.1 Functions ............................................................................................................................... 233
3.2 The Graph of a Function ....................................................................................................... 251
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
VERIFIEDBRAINBOOSTER
, VE
R
Chapter 4 Linear and Quadratic Functions
IF
4.1 Properties of Linear Functions and Linear Models ............................................................... 331
4.2 Building Linear Functions from Data ................................................................................... 342
IE
4.3 Quadratic Functions and Their Properties ............................................................................. 348
4.4 Build Quadratic Models from Verbal Descriptions and from Data ...................................... 371
D
4.5 Inequalities Involving Quadratic Functions .......................................................................... 379
Chapter Review ............................................................................................................................ 399
BR
Chapter Test ................................................................................................................................. 407
Cumulative Review ...................................................................................................................... 409
Chapter Projects ........................................................................................................................... 412
AI
Chapter 5 Polynomial and Rational Functions
N
5.1 Polynomial Functions............................................................................................................ 415
BO
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
O
5.6 The Real Zeros of a Polynomial Function............................................................................. 528
ST
5.7 Complex Zeros; Fundamental Theorem of Algebra .............................................................. 559
Chapter Review ............................................................................................................................ 568
Chapter Test ................................................................................................................................. 583
ER
Cumulative Review ...................................................................................................................... 587
Chapter Projects ........................................................................................................................... 592
Chapter 6 Exponential and Logarithmic Functions
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
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
Chapter Test ................................................................................................................................. 741
Cumulative Review ...................................................................................................................... 745
Chapter Projects ........................................................................................................................... 748
VERIFIEDBRAINBOOSTER
R
INSTRUCTOR’S SOLUTIONS
IF
IE
MANUAL
D
BR
TIM BRITT
Jackson State Community College
AI
N
BO
ALGEBRA AND
O
ST
TRIGONOMETRY
ER
E LEVENTH E DITION
Michael Sullivan
Chicago State University
VERIFIEDBRAINBOOSTER
, VE
R
IF
IE
D
BR
AI
N
BO
The author and publisher of this book have used their best efforts in preparing this book. These efforts include the
O
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
ST
contained in this book. The author and publisher shall not be liable in any event for incidental or consequential damages
in connection with, or arising out of, the furnishing, performance, or use of these programs.
ER
Reproduced by Pearson from electronic files supplied by the author.
Copyright © 2020, 2016, 2012 Pearson Education, Inc.
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.
ISBN-13: 978-0-13-518932-0
ISBN-10: 0-13-518932-2
VERIFIEDBRAINBOOSTER
, VE
R
Table of Contents
IF
IE
Chapter R Review
R.1 Real Numbers ........................................................................................................................... 1
D
R.2 Algebra Essentials .................................................................................................................... 5
R.3 Geometry Essentials ............................................................................................................... 11
BR
R.4 Polynomials ............................................................................................................................ 16
R.5 Factoring Polynomials ............................................................................................................ 23
R.6 Synthetic Division .................................................................................................................. 28
AI
R.7 Rational Expressions .............................................................................................................. 30
R.8 nth Roots; Rational Exponents ............................................................................................... 40
N
Chapter 1 Equations and Inequalities
BO
1.1 Linear Equations ..................................................................................................................... 50
1.2 Quadratic Equations ................................................................................................................ 68
1.3 Complex Numbers; Quadratic Equations in the Complex Number System............................ 87
O
1.4 Radical Equations; Equations Quadratic in Form; Factorable Equations ............................... 93
1.5 Solving Inequalities ............................................................................................................... 116
ST
1.6 Equations and Inequalities Involving Absolute Value .......................................................... 127
1.7 Problem Solving: Interest, Mixture, Uniform Motion, Constant Rate Job Applications ...... 137
Chapter Review ............................................................................................................................ 145
ER
Chapter Test ................................................................................................................................. 154
Chapter Projects ........................................................................................................................... 156
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
Chapter Test ................................................................................................................................. 228
Cumulative Review ...................................................................................................................... 230
Chapter Project ............................................................................................................................. 232
Chapter 3 Functions and Their Graphs
3.1 Functions ............................................................................................................................... 233
3.2 The Graph of a Function ....................................................................................................... 251
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
VERIFIEDBRAINBOOSTER
, VE
R
Chapter 4 Linear and Quadratic Functions
IF
4.1 Properties of Linear Functions and Linear Models ............................................................... 331
4.2 Building Linear Functions from Data ................................................................................... 342
IE
4.3 Quadratic Functions and Their Properties ............................................................................. 348
4.4 Build Quadratic Models from Verbal Descriptions and from Data ...................................... 371
D
4.5 Inequalities Involving Quadratic Functions .......................................................................... 379
Chapter Review ............................................................................................................................ 399
BR
Chapter Test ................................................................................................................................. 407
Cumulative Review ...................................................................................................................... 409
Chapter Projects ........................................................................................................................... 412
AI
Chapter 5 Polynomial and Rational Functions
N
5.1 Polynomial Functions............................................................................................................ 415
BO
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
O
5.6 The Real Zeros of a Polynomial Function............................................................................. 528
ST
5.7 Complex Zeros; Fundamental Theorem of Algebra .............................................................. 559
Chapter Review ............................................................................................................................ 568
Chapter Test ................................................................................................................................. 583
ER
Cumulative Review ...................................................................................................................... 587
Chapter Projects ........................................................................................................................... 592
Chapter 6 Exponential and Logarithmic Functions
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
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
Chapter Test ................................................................................................................................. 741
Cumulative Review ...................................................................................................................... 745
Chapter Projects ........................................................................................................................... 748
VERIFIEDBRAINBOOSTER
