Solution Manual for College Algebra Enhanced with Graphing Utilities, 8th Edition

Name: Solution Manual for College Algebra Enhanced with Graphing Utilities, 8th Edition
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SOLUTIONS MANUAL
T IM B RITT
Jackson State Community College
C OLLEGE A LGEBRA
E NHANCED WITH G RAPHING U TILITIES
EIGHTH EDITION
Michael Sullivan
Chicago State University
Michael Sullivan III
Joliet Junior College

Table of Contents
Chapter R Review
R.1 Real Numbers ............................................................................................................................1
R.2 Algebra Essentials .....................................................................................................................5
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 Graphs, Equations, and Inequalities
1.1 Graphing Utilities; Introduction to Graphing Equations.........................................................50
1.2 Solving Equations Using a Graphing Utility; Linear and Rational Equations .......................57
1.3 Quadratic Equations ................................................................................................................71
1.4 Complex Numbers; Quadratic Equations in the Complex Number System ...........................90
1.5 Radical Equations; Equations Quadratic in Form; Absolute Value Equations;
Factorable Equations ...............................................................................................................96
1.6 Problem Solving: Interest, Mixture, Uniform Motion, Constant Rate Job Applications......117
1.7 Solving Inequalities...............................................................................................................125
Chapter Review .............................................................................................................................137
Chapter Test...................................................................................................................................147
Chapter Projects .............................................................................................................................151
Chapter 2 Graphs
2.1 The Distance and Midpoint Formulas ...................................................................................152
2.2 Intercepts; Symmetry; Graphing Key Equations ..................................................................165
2.3 Lines ......................................................................................................................................182
2.4 Circles ...................................................................................................................................200
2.5 Variation................................................................................................................................215
Chapter Review .............................................................................................................................220
Chapter Test ...................................................................................................................................226
Cumulative Review .......................................................................................................................228
Chapter Projects .............................................................................................................................230
Chapter 3 Functions and Their Graphs
3.1 Functions ...............................................................................................................................231
3.2 The Graph of a Function .......................................................................................................249
3.3 Properties of Functions .........................................................................................................258
3.4 Library of Functions; Piecewise-defined Functions .............................................................275
3.5 Graphing Techniques: Transformations................................................................................287
3.6 Mathematical Models: Building Functions ...........................................................................305
Chapter Review .............................................................................................................................313
Chapter Test ...................................................................................................................................320
Cumulative Review .......................................................................................................................323
Chapter Projects.............................................................................................................................327

Chapter 4 Linear and Quadratic Functions
4.1 Properties of Linear Functions and Linear Models ...............................................................329
4.2 Building Linear Models from Data .......................................................................................340
4.3 Quadratic Functions and Their Properties ............................................................................346
4.4 Building Quadratic Models from Verbal Descriptions and from Data .................................370
4.5 Inequalities Involving Quadratic Functions ..........................................................................378
Chapter Review .............................................................................................................................397
Chapter Test ...................................................................................................................................405
Cumulative Review .......................................................................................................................408
Chapter Projects .............................................................................................................................411
Chapter 5 Polynomial and Rational Functions
5.1 Polynomial Functions ...........................................................................................................414
5.2 The Graph of a Polynomial Function; Models......................................................................425
5.3 The Real Zeros of a Polynomial Function ............................................................................445
5.4 Complex Zeros; Fundamental Theorem of Algebra .............................................................482
5.5 Properties of Rational Functions ...........................................................................................491
5.6 The Graph of a Rational Function.........................................................................................501
5.7 Polynomial and Rational Inequalities ...................................................................................557
Chapter Review .............................................................................................................................579
Chapter Test ...................................................................................................................................593
Cumulative Review .......................................................................................................................597
Chapter Projects .............................................................................................................................602
Chapter 6 Exponential and Logarithmic Functions
6.1 Composite Functions.............................................................................................................603
6.2 One-to-One Functions; Inverse Functions ............................................................................621
6.3 Exponential Functions...........................................................................................................644
6.4 Logarithmic Functions ..........................................................................................................665
6.5 Properties of Logarithms .......................................................................................................687
6.6 Logarithmic and Exponential Equations ...............................................................................696
6.7 Financial Models ...................................................................................................................717
6.8 Exponential Growth and Decay Models; Newton’s Law; Logistic Growth
and Decay Models .................................................................................................................725
6.9 Building Exponential, Logarithmic, and Logistic Models from Data ..................................736
Chapter Review .............................................................................................................................741
Chapter Test ...................................................................................................................................753
Cumulative Review .......................................................................................................................757
Chapter Projects .............................................................................................................................760

Chapter 7 Analytic Geometry
7.2 The Parabola .........................................................................................................................763
7.3 The Ellipse ............................................................................................................................778
7.4 The Hyperbola.......................................................................................................................796
Chapter Review .............................................................................................................................816
Chapter Test ...................................................................................................................................821
Cumulative Review .......................................................................................................................823
Chapter Projects .............................................................................................................................825
Chapter 8 Systems of Equations and Inequalities
8.1 Systems of Linear Equations: Substitution and Elimination ................................................828
8.2 Systems of Linear Equations: Matrices ................................................................................851
8.3 Systems of Linear Equations: Determinants .........................................................................876
8.4 Matrix Algebra ......................................................................................................................890
8.5 Partial Fraction Decomposition ............................................................................................909
8.6 Systems of Nonlinear Equations ...........................................................................................928
8.7 Systems of Inequalities .........................................................................................................956
8.8 Linear Programming .............................................................................................................971
Chapter Review .............................................................................................................................984
Chapter Test ...................................................................................................................................999
Cumulative Review .....................................................................................................................1008
Chapter Projects...........................................................................................................................1011
Chapter 9 Sequences; Induction; the Binomial Theorem
9.1 Sequences ............................................................................................................................1014
9.2 Arithmetic Sequences .........................................................................................................1028
9.3 Geometric Sequences; Geometric Series ............................................................................1037
9.4 Mathematical Induction ......................................................................................................1048
9.5 The Binomial Theorem .......................................................................................................1057
Chapter Review ...........................................................................................................................1064
Chapter Test .................................................................................................................................1068
Cumulative Review .....................................................................................................................1071
Chapter Projects ...........................................................................................................................1073
Chapter 10 Counting and Probability
10.1 Counting ..............................................................................................................................1076
10.2 Permutations and Combinations .........................................................................................1079
10.3 Probability ...........................................................................................................................1084
Chapter Review ...........................................................................................................................1091
Chapter Test .................................................................................................................................1093
Cumulative Review .....................................................................................................................1094
Chapter Projects ...........................................................................................................................1097

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