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 Equations and Inequalities
M
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
EL
1.5 Solving Inequalities ............................................................................................................... 116
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
AN
Chapter Test ................................................................................................................................. 154
Chapter Projects ........................................................................................................................... 156
Chapter 2 Graphs
2.1 The Distance and Midpoint Formulas ................................................................................... 157
IE
2.2 Graphs of Equations in Two Variables; Intercepts; Symmetry ............................................. 170
2.3 Lines ...................................................................................................................................... 184
2.4 Circles ................................................................................................................................... 202
2.5 Variation................................................................................................................................ 216
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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
,Chapter 4 Linear and Quadratic Functions
4.1 Properties of Linear Functions and Linear Models ............................................................... 331
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
Chapter Review ............................................................................................................................ 399
Chapter Test ................................................................................................................................. 407
Cumulative Review ...................................................................................................................... 409
Chapter Projects ........................................................................................................................... 412
Chapter 5 Polynomial and Rational Functions
5.1 Polynomial Functions............................................................................................................ 415
M
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
EL
5.7 Complex Zeros; Fundamental Theorem of Algebra .............................................................. 559
Chapter Review ............................................................................................................................ 568
Chapter Test ................................................................................................................................. 583
Cumulative Review ...................................................................................................................... 587
AN
Chapter Projects ........................................................................................................................... 592
Chapter 6 Exponential and Logarithmic Functions
6.1 Composite Functions ............................................................................................................. 594
6.2 One-to-One Functions; Inverse Functions ............................................................................ 612
IE
6.3 Exponential Functions ........................................................................................................... 634
6.4 Logarithmic Functions .......................................................................................................... 655
6.5 Properties of Logarithms ....................................................................................................... 677
6.6 Logarithmic and Exponential Equations ............................................................................... 686
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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
,Chapter 7 Trigonometric Functions
7.1 Angles, Arc Length, and Circular Motion ............................................................................. 751
7.2 Right Triangle Trigonometry ................................................................................................ 760
7.3 Computing the Values of Trigonometric Functions of Acute Angles ................................... 776
7.4 Trigonometric Functions of Any Angle ................................................................................ 789
7.5 Unit Circle Approach: Properties of the Trigonometric Functions ....................................... 805
7.6 Graphs of the Sine and Cosine Functions ............................................................................. 814
7.7 Graphs of the Tangent, Cotangent, Cosecant, and Secant Functions .................................... 836
7.8 Phase Shift; Sinusoidal Curve Fitting ................................................................................... 846
Chapter Review ............................................................................................................................ 857
Chapter Test ................................................................................................................................. 866
Cumulative Review ...................................................................................................................... 870
Chapter Projects ........................................................................................................................... 874
Chapter 8 Analytic Trigonometry
M
8.1 The Inverse Sine, Cosine, and Tangent Functions ................................................................ 877
8.2 The Inverse Trigonometric Functions (Continued) ............................................................... 890
8.3 Trigonometric Equations ....................................................................................................... 902
8.4 Trigonometric Identities ........................................................................................................ 923
EL
8.5 Sum and Difference Formulas............................................................................................... 936
8.6 Double-angle and Half-angle Formulas ................................................................................ 961
8.7 Product-to-Sum and Sum-to-Product Formulas .................................................................... 987
Chapter Review .......................................................................................................................... 1000
AN
Chapter Test ............................................................................................................................... 1015
Cumulative Review .................................................................................................................... 1020
Chapter Projects ......................................................................................................................... 1026
Chapter 9 Applications of Trigonometric Functions
IE
9.1 Applications Involving Right Triangles .............................................................................. 1030
9.2 The Law of Sines ................................................................................................................ 1038
9.3 The Law of Cosines ............................................................................................................ 1053
9.4 Area of a Triangle ............................................................................................................... 1065
??
9.5 Simple Harmonic Motion; Damped Motion; Combining Waves ........................................ 1075
Chapter Review .......................................................................................................................... 1085
Chapter Test ............................................................................................................................... 1091
Cumulative Review .................................................................................................................... 1094
??
Chapter Projects ......................................................................................................................... 1100
Chapter 10 Polar Coordinates; Vectors
10.1 Polar Coordinates .............................................................................................................. 1104
10.2 Polar Equations and Graphs .............................................................................................. 1113
10.3 The Complex Plane; De Moivre’s Theorem ..................................................................... 1143
10.4 Vectors .............................................................................................................................. 1156
10.5 The Dot Product ................................................................................................................ 1169
Chapter Review .......................................................................................................................... 1175
Chapter Test ............................................................................................................................... 1183
Cumulative Review .................................................................................................................... 1186
Chapter Projects ......................................................................................................................... 1189
, Chapter 11 Analytic Geometry
11.2 The Parabola...................................................................................................................... 1193
11.3 The Ellipse ........................................................................................................................ 1208
11.4 The Hyperbola ................................................................................................................... 1225
11.5 Rotation of Axes; General Form of a Conic...................................................................... 1245
11.6 Polar Equations of Conics ................................................................................................. 1258
11.7 Plane Curves and Parametric Equations ............................................................................ 1267
Chapter Review .......................................................................................................................... 1282
Chapter Test ............................................................................................................................... 1291
Cumulative Review .................................................................................................................... 1296
Chapter Projects ......................................................................................................................... 1298
Chapter 12 Systems of Equations and Inequalities
12.1 Systems of Linear Equations: Substitution and Elimination ............................................. 1302
12.2 Systems of Linear Equations: Matrices ............................................................................. 1325
M
12.3 Systems of Linear Equations: Determinants ..................................................................... 1350
12.4 Matrix Algebra .................................................................................................................. 1364
12.5 Partial Fraction Decomposition ......................................................................................... 1383
12.6 Systems of Nonlinear Equations ....................................................................................... 1402
EL
12.7 Systems of Inequalities...................................................................................................... 1430
12.8 Linear Programming ......................................................................................................... 1446
Chapter Review .......................................................................................................................... 1459
Chapter Test ............................................................................................................................... 1474
AN
Cumulative Review .................................................................................................................... 1483
Chapter Projects ......................................................................................................................... 1486
Chapter 13 Sequences; Induction; the Binomial Theorem
13.1 Sequences .......................................................................................................................... 1489
IE
13.2 Arithmetic Sequences........................................................................................................ 1499
13.3 Geometric Sequences; Geometric Series .......................................................................... 1508
13.4 Mathematical Induction..................................................................................................... 1520
13.5 The Binomial Theorem ..................................................................................................... 1529
??
Chapter Review .......................................................................................................................... 1536
Chapter Test ............................................................................................................................... 1540
Cumulative Review .................................................................................................................... 1543
Chapter Projects ......................................................................................................................... 1546
??
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 Equations and Inequalities
M
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
EL
1.5 Solving Inequalities ............................................................................................................... 116
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
AN
Chapter Test ................................................................................................................................. 154
Chapter Projects ........................................................................................................................... 156
Chapter 2 Graphs
2.1 The Distance and Midpoint Formulas ................................................................................... 157
IE
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
,Chapter 4 Linear and Quadratic Functions
4.1 Properties of Linear Functions and Linear Models ............................................................... 331
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
Chapter Review ............................................................................................................................ 399
Chapter Test ................................................................................................................................. 407
Cumulative Review ...................................................................................................................... 409
Chapter Projects ........................................................................................................................... 412
Chapter 5 Polynomial and Rational Functions
5.1 Polynomial Functions............................................................................................................ 415
M
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
EL
5.7 Complex Zeros; Fundamental Theorem of Algebra .............................................................. 559
Chapter Review ............................................................................................................................ 568
Chapter Test ................................................................................................................................. 583
Cumulative Review ...................................................................................................................... 587
AN
Chapter Projects ........................................................................................................................... 592
Chapter 6 Exponential and Logarithmic Functions
6.1 Composite Functions ............................................................................................................. 594
6.2 One-to-One Functions; Inverse Functions ............................................................................ 612
IE
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
,Chapter 7 Trigonometric Functions
7.1 Angles, Arc Length, and Circular Motion ............................................................................. 751
7.2 Right Triangle Trigonometry ................................................................................................ 760
7.3 Computing the Values of Trigonometric Functions of Acute Angles ................................... 776
7.4 Trigonometric Functions of Any Angle ................................................................................ 789
7.5 Unit Circle Approach: Properties of the Trigonometric Functions ....................................... 805
7.6 Graphs of the Sine and Cosine Functions ............................................................................. 814
7.7 Graphs of the Tangent, Cotangent, Cosecant, and Secant Functions .................................... 836
7.8 Phase Shift; Sinusoidal Curve Fitting ................................................................................... 846
Chapter Review ............................................................................................................................ 857
Chapter Test ................................................................................................................................. 866
Cumulative Review ...................................................................................................................... 870
Chapter Projects ........................................................................................................................... 874
Chapter 8 Analytic Trigonometry
M
8.1 The Inverse Sine, Cosine, and Tangent Functions ................................................................ 877
8.2 The Inverse Trigonometric Functions (Continued) ............................................................... 890
8.3 Trigonometric Equations ....................................................................................................... 902
8.4 Trigonometric Identities ........................................................................................................ 923
EL
8.5 Sum and Difference Formulas............................................................................................... 936
8.6 Double-angle and Half-angle Formulas ................................................................................ 961
8.7 Product-to-Sum and Sum-to-Product Formulas .................................................................... 987
Chapter Review .......................................................................................................................... 1000
AN
Chapter Test ............................................................................................................................... 1015
Cumulative Review .................................................................................................................... 1020
Chapter Projects ......................................................................................................................... 1026
Chapter 9 Applications of Trigonometric Functions
IE
9.1 Applications Involving Right Triangles .............................................................................. 1030
9.2 The Law of Sines ................................................................................................................ 1038
9.3 The Law of Cosines ............................................................................................................ 1053
9.4 Area of a Triangle ............................................................................................................... 1065
??
9.5 Simple Harmonic Motion; Damped Motion; Combining Waves ........................................ 1075
Chapter Review .......................................................................................................................... 1085
Chapter Test ............................................................................................................................... 1091
Cumulative Review .................................................................................................................... 1094
??
Chapter Projects ......................................................................................................................... 1100
Chapter 10 Polar Coordinates; Vectors
10.1 Polar Coordinates .............................................................................................................. 1104
10.2 Polar Equations and Graphs .............................................................................................. 1113
10.3 The Complex Plane; De Moivre’s Theorem ..................................................................... 1143
10.4 Vectors .............................................................................................................................. 1156
10.5 The Dot Product ................................................................................................................ 1169
Chapter Review .......................................................................................................................... 1175
Chapter Test ............................................................................................................................... 1183
Cumulative Review .................................................................................................................... 1186
Chapter Projects ......................................................................................................................... 1189
, Chapter 11 Analytic Geometry
11.2 The Parabola...................................................................................................................... 1193
11.3 The Ellipse ........................................................................................................................ 1208
11.4 The Hyperbola ................................................................................................................... 1225
11.5 Rotation of Axes; General Form of a Conic...................................................................... 1245
11.6 Polar Equations of Conics ................................................................................................. 1258
11.7 Plane Curves and Parametric Equations ............................................................................ 1267
Chapter Review .......................................................................................................................... 1282
Chapter Test ............................................................................................................................... 1291
Cumulative Review .................................................................................................................... 1296
Chapter Projects ......................................................................................................................... 1298
Chapter 12 Systems of Equations and Inequalities
12.1 Systems of Linear Equations: Substitution and Elimination ............................................. 1302
12.2 Systems of Linear Equations: Matrices ............................................................................. 1325
M
12.3 Systems of Linear Equations: Determinants ..................................................................... 1350
12.4 Matrix Algebra .................................................................................................................. 1364
12.5 Partial Fraction Decomposition ......................................................................................... 1383
12.6 Systems of Nonlinear Equations ....................................................................................... 1402
EL
12.7 Systems of Inequalities...................................................................................................... 1430
12.8 Linear Programming ......................................................................................................... 1446
Chapter Review .......................................................................................................................... 1459
Chapter Test ............................................................................................................................... 1474
AN
Cumulative Review .................................................................................................................... 1483
Chapter Projects ......................................................................................................................... 1486
Chapter 13 Sequences; Induction; the Binomial Theorem
13.1 Sequences .......................................................................................................................... 1489
IE
13.2 Arithmetic Sequences........................................................................................................ 1499
13.3 Geometric Sequences; Geometric Series .......................................................................... 1508
13.4 Mathematical Induction..................................................................................................... 1520
13.5 The Binomial Theorem ..................................................................................................... 1529
??
Chapter Review .......................................................................................................................... 1536
Chapter Test ............................................................................................................................... 1540
Cumulative Review .................................................................................................................... 1543
Chapter Projects ......................................................................................................................... 1546
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