, INSTRUCTOR’S
SOLUTIONS MANUAL
TIM BRITT
Jackson State Community College
C OLLEGE A LGEBRA :
C ONCEPTS T HROUGH F UNCTIONS
FIFTH EDITION
MICHAEL SULLIVAN
CHICAGO STATE UNIVERSITY
MICHAEL SULLIVAN, III
JOLIET JUNIOR COLLEGE
, Table of Contents
Chapter F: Foundations: A Prelude to functions
F.1 The Distance and Midpoint Formulas.......................................................................................... 1
F.2 Graphs of Equations in Two Variables; Intercepts; Symmetry ................................................. 13
F.3 Lines .......................................................................................................................................... 30
F.4 Circles ........................................................................................................................................ 48
Chapter Project ................................................................................................................................. 61
Chapter 1: Functions and Their Graphs
1.1 Functions .................................................................................................................................... 62
1.2 The Graph of a Function ............................................................................................................ 79
1.3 Properties of Functions .............................................................................................................. 88
1.4 Library of Functions; Piecewise-defined Functions................................................................. 103
1.5 Graphing Techniques: Transformations................................................................................... 115
1.6 Mathematical Models: Building Functions .............................................................................. 133
1.7 Building Mathematical Models Using Variation ..................................................................... 139
Chapter Review............................................................................................................................... 143
Chapter Test .................................................................................................................................... 151
Chapter Projects .............................................................................................................................. 155
Chapter 2: Linear and Quadratic Functions
2.1 Properties of Linear Functions and Linear Models .................................................................. 157
2.2 Building Linear Models from Data .......................................................................................... 169
2.3 Quadratic Functions and Their Zeros....................................................................................... 175
2.4 Properties of Quadratic Functions............................................................................................ 194
2.5 Inequalities Involving Quadratic Functions ............................................................................. 218
2.6 Building Quadratic Models from Verbal Descriptions and from Data .................................... 238
2.7 Complex Zeros of a Quadratic Function .................................................................................. 246
2.8 Equations and Inequalities Involving the Absolute Value Function ........................................ 251
Chapter Review............................................................................................................................... 262
Chapter Test .................................................................................................................................... 273
Cumulative Review......................................................................................................................... 277
Chapter Projects .............................................................................................................................. 280
Chapter 3: Polynomial and Rational Functions
3.1 Polynomial Functions .............................................................................................................. 283
3.2 Graphing Polynomial Functions; Models ................................................................................ 294
3.3 The Real Zeros of a Polynomial Function ............................................................................... 310
3.4 Complex Zeros; Fundamental Theorem of Algebra ................................................................ 341
3.5 Properties of Rational Functions .............................................................................................. 350
3.6 The Graph of a Rational Function............................................................................................ 360
3.7 Polynomial and Rational Inequalities ...................................................................................... 417
Chapter Review............................................................................................................................... 437
Chapter Test .................................................................................................................................... 452
Cumulative Review......................................................................................................................... 457
Chapter Projects .............................................................................................................................. 461
, Chapter 4: Exponential and Logarithmic Functions
4.1 Composite Functions ............................................................................................................... 463
4.2 One-to-One Functions; Inverse Functions ............................................................................... 481
4.3 Exponential Functions ............................................................................................................. 504
4.4 Logarithmic Functions ............................................................................................................. 525
4.5 Properties of Logarithms.......................................................................................................... 547
4.6 Logarithmic and Exponential Equations .................................................................................. 556
4.7 Financial Models...................................................................................................................... 577
4.8 Exponential Growth and Decay Models; Newton’s Law; Logistic Growth
and Decay Models............................................................................................................ 585
4.9 Building Exponential, Logarithmic, and Logistic Models from Data ...................................... 595
Chapter Review............................................................................................................................... 600
Chapter Test .................................................................................................................................... 612
Cumulative Review......................................................................................................................... 616
Chapter Projects .............................................................................................................................. 619
Chapter 5: Analytic Geometry
5.2 The Parabola ............................................................................................................................ 622
5.3 The Ellipse ............................................................................................................................... 637
5.4 The Hyperbola ......................................................................................................................... 655
Chapter Review............................................................................................................................... 675
Chapter Test .................................................................................................................................... 680
Cumulative Review......................................................................................................................... 682
Chapter Projects .............................................................................................................................. 684
Chapter 6: Systems of Equations and Inequalities
6.1 Systems of Linear Equations: Substitution and Elimination .................................................... 687
6.2 Systems of Linear Equations: Matrices.................................................................................... 710
6.3 Systems of Linear Equations: Determinants ............................................................................ 735
6.4 Matrix Algebra ......................................................................................................................... 748
6.5 Partial Fraction Decomposition ............................................................................................... 767
6.6 Systems of Nonlinear Equations .............................................................................................. 786
6.7 Systems of Inequalities ............................................................................................................ 814
6.8 Linear Programming ................................................................................................................ 829
Chapter Review............................................................................................................................... 843
Chapter Test .................................................................................................................................... 858
Cumulative Review......................................................................................................................... 866
Chapter Projects .............................................................................................................................. 870
Chapter 7: Sequence; Induction; the Binomial Theorem
7.1 Sequences................................................................................................................................. 872
7.2 Arithmetic Sequences .............................................................................................................. 882
7.3 Geometric Sequences; Geometric Series ................................................................................. 891
7.4 Mathematical Induction ........................................................................................................... 903
7.5 The Binomial Theorem ............................................................................................................ 912
Chapter Review............................................................................................................................... 918
Chapter Test .................................................................................................................................... 923
Cumulative Review......................................................................................................................... 926
Chapter Projects .............................................................................................................................. 928
SOLUTIONS MANUAL
TIM BRITT
Jackson State Community College
C OLLEGE A LGEBRA :
C ONCEPTS T HROUGH F UNCTIONS
FIFTH EDITION
MICHAEL SULLIVAN
CHICAGO STATE UNIVERSITY
MICHAEL SULLIVAN, III
JOLIET JUNIOR COLLEGE
, Table of Contents
Chapter F: Foundations: A Prelude to functions
F.1 The Distance and Midpoint Formulas.......................................................................................... 1
F.2 Graphs of Equations in Two Variables; Intercepts; Symmetry ................................................. 13
F.3 Lines .......................................................................................................................................... 30
F.4 Circles ........................................................................................................................................ 48
Chapter Project ................................................................................................................................. 61
Chapter 1: Functions and Their Graphs
1.1 Functions .................................................................................................................................... 62
1.2 The Graph of a Function ............................................................................................................ 79
1.3 Properties of Functions .............................................................................................................. 88
1.4 Library of Functions; Piecewise-defined Functions................................................................. 103
1.5 Graphing Techniques: Transformations................................................................................... 115
1.6 Mathematical Models: Building Functions .............................................................................. 133
1.7 Building Mathematical Models Using Variation ..................................................................... 139
Chapter Review............................................................................................................................... 143
Chapter Test .................................................................................................................................... 151
Chapter Projects .............................................................................................................................. 155
Chapter 2: Linear and Quadratic Functions
2.1 Properties of Linear Functions and Linear Models .................................................................. 157
2.2 Building Linear Models from Data .......................................................................................... 169
2.3 Quadratic Functions and Their Zeros....................................................................................... 175
2.4 Properties of Quadratic Functions............................................................................................ 194
2.5 Inequalities Involving Quadratic Functions ............................................................................. 218
2.6 Building Quadratic Models from Verbal Descriptions and from Data .................................... 238
2.7 Complex Zeros of a Quadratic Function .................................................................................. 246
2.8 Equations and Inequalities Involving the Absolute Value Function ........................................ 251
Chapter Review............................................................................................................................... 262
Chapter Test .................................................................................................................................... 273
Cumulative Review......................................................................................................................... 277
Chapter Projects .............................................................................................................................. 280
Chapter 3: Polynomial and Rational Functions
3.1 Polynomial Functions .............................................................................................................. 283
3.2 Graphing Polynomial Functions; Models ................................................................................ 294
3.3 The Real Zeros of a Polynomial Function ............................................................................... 310
3.4 Complex Zeros; Fundamental Theorem of Algebra ................................................................ 341
3.5 Properties of Rational Functions .............................................................................................. 350
3.6 The Graph of a Rational Function............................................................................................ 360
3.7 Polynomial and Rational Inequalities ...................................................................................... 417
Chapter Review............................................................................................................................... 437
Chapter Test .................................................................................................................................... 452
Cumulative Review......................................................................................................................... 457
Chapter Projects .............................................................................................................................. 461
, Chapter 4: Exponential and Logarithmic Functions
4.1 Composite Functions ............................................................................................................... 463
4.2 One-to-One Functions; Inverse Functions ............................................................................... 481
4.3 Exponential Functions ............................................................................................................. 504
4.4 Logarithmic Functions ............................................................................................................. 525
4.5 Properties of Logarithms.......................................................................................................... 547
4.6 Logarithmic and Exponential Equations .................................................................................. 556
4.7 Financial Models...................................................................................................................... 577
4.8 Exponential Growth and Decay Models; Newton’s Law; Logistic Growth
and Decay Models............................................................................................................ 585
4.9 Building Exponential, Logarithmic, and Logistic Models from Data ...................................... 595
Chapter Review............................................................................................................................... 600
Chapter Test .................................................................................................................................... 612
Cumulative Review......................................................................................................................... 616
Chapter Projects .............................................................................................................................. 619
Chapter 5: Analytic Geometry
5.2 The Parabola ............................................................................................................................ 622
5.3 The Ellipse ............................................................................................................................... 637
5.4 The Hyperbola ......................................................................................................................... 655
Chapter Review............................................................................................................................... 675
Chapter Test .................................................................................................................................... 680
Cumulative Review......................................................................................................................... 682
Chapter Projects .............................................................................................................................. 684
Chapter 6: Systems of Equations and Inequalities
6.1 Systems of Linear Equations: Substitution and Elimination .................................................... 687
6.2 Systems of Linear Equations: Matrices.................................................................................... 710
6.3 Systems of Linear Equations: Determinants ............................................................................ 735
6.4 Matrix Algebra ......................................................................................................................... 748
6.5 Partial Fraction Decomposition ............................................................................................... 767
6.6 Systems of Nonlinear Equations .............................................................................................. 786
6.7 Systems of Inequalities ............................................................................................................ 814
6.8 Linear Programming ................................................................................................................ 829
Chapter Review............................................................................................................................... 843
Chapter Test .................................................................................................................................... 858
Cumulative Review......................................................................................................................... 866
Chapter Projects .............................................................................................................................. 870
Chapter 7: Sequence; Induction; the Binomial Theorem
7.1 Sequences................................................................................................................................. 872
7.2 Arithmetic Sequences .............................................................................................................. 882
7.3 Geometric Sequences; Geometric Series ................................................................................. 891
7.4 Mathematical Induction ........................................................................................................... 903
7.5 The Binomial Theorem ............................................................................................................ 912
Chapter Review............................................................................................................................... 918
Chapter Test .................................................................................................................................... 923
Cumulative Review......................................................................................................................... 926
Chapter Projects .............................................................................................................................. 928
