Precalculus, 2nd Edition

Cover Page......Page 1
Title Page......Page 2
Copyright Page......Page 3
Brief Contents......Page 4
Dedication......Page 5
Preface......Page 7
Acknowledgments......Page 26
Contents......Page 28
Index of Applications......Page 36
CHAPTER 1: Equations and Inequalities......Page 42
1.1 Linear Equations, Formulas, and Problem Solving......Page 43
Technology Highlight: Using a Graphing Calculator as an Investigative Tool......Page 50
1.2 Linear Inequalities in One Variable......Page 55
1.3 Absolute Value Equations and Inequalities......Page 65
Technology Highlight: Absolute Value Equations and Inequalities......Page 69
Mid-Chapter Check......Page 72
Reinforcing Basic Concepts: Using Distance to Understand Absolute Value Equations and Inequalities......Page 73
1.4 Complex Numbers......Page 74
1.5 Solving Quadratic Equations......Page 83
Technology Highlight: The Discriminant......Page 92
1.6 Solving Other Types of Equations......Page 97
Summary and Concept Review......Page 111
Practice Test......Page 116
Calculator Exploration and Discovery: Evaluating Expressions and Looking for Patterns......Page 117
Strengthening Core Skills: An Alternative Method for Checking Solutions to Quadratic Equations......Page 118
Connections to Calculus: Solving Various Types of Equations; Absolute Value Inequalities and Delta/Epsilon form......Page 120
CHAPTER 2: Relations, Functions, and Graphs......Page 124
2.1 Rectangular Coordinates; Graphing Circles and Other Relations......Page 125
Technology Highlight: The Graph of a Circle......Page 133
2.2 Graphs of Linear Equations......Page 138
Technology Highlight: Linear Equations, Window Size, and Friendly Windows......Page 146
2.3 Linear Graphs and Rates of Change......Page 151
2.4 Functions, Function Notation, and the Graph of a Function......Page 163
Mid-Chapter Check......Page 178
2.5 Analyzing the Graph of a Function......Page 179
Technology Highlight: Locating Zeroes, Maximums, and Minimums......Page 190
2.6 The Toolbox Functions and Transformations......Page 198
Technology Highlight: Function Families......Page 207
2.7 Piecewise-Defined Fun......Page 213
Technology Highlight: Piecewise-Defined Functions......Page 220
2.8 The Algebra and Composition of Functions......Page 227
Technology Highlight: Composite Functions......Page 237
Summary and Concept Review......Page 243
Mixed Review......Page 250
Practice Test......Page 252
Calculator Exploration and Discovery: Using a Simple Program to Explore Transformations......Page 253
Strengthening Core Skills: Transformations via Composition......Page 254
Cumulative Review: Chapters 1–2......Page 255
Connections to Calculus: Rates of Change and the Difference Quotient; Transformations and the Area Under a Curve......Page 256
CHAPTER 3: Polynomial and Rational Functions......Page 260
3.1 Quadratic Functions and Applications......Page 261
Technology Highlight: Estimating Irrational Zeroes......Page 266
3.2 Synthetic Division; The Remainder and Factor Theorems......Page 271
3.3 The Zeroes of Polynomial Functions......Page 283
Technology Highlight: The Intermediate Value Theorem and Split Screen Viewing......Page 293
3.4 Graphing Polynomial Functions......Page 298
Reinforcing Basic Concepts: Approximating Real Zeroes......Page 312
3.5 Graphing Rational Functions......Page 313
Technology Highlight: Rational Functions and Appropriate Domains......Page 323
3.6 Additional Insights into Rational Functions......Page 330
Technology Highlight: Removable Discontinuities......Page 338
3.7 Polynomial and Rational Inequalities......Page 344
Technology Highlight: Polynomial and Rational Inequalities......Page 351
3.8 Variation: Function Models in Action......Page 357
Summary and Concept Review......Page 367
Mixed Review......Page 372
Practice Test......Page 373
Strengthening Core Skills: Solving Inequalities Using the Push Principle......Page 375
Cumulative Review: Chapters 1–3......Page 376
Connections to Calculus: Graphing Techniques......Page 378
CHAPTER 4: Exponential and Logarithmic Functions......Page 382
4.1 One-to-One and Inverse Functions......Page 383
Technology Highlight: Investigating Inverse Functions......Page 390
4.2 Exponential Functions......Page 395
Technology Highlight: Solving Exponential Equations Graphically......Page 402
4.3 Logarithms and Logarithmic Functions......Page 407
Mid-Chapter Check......Page 420
Reinforcing Basic Concepts: Linear and Logarithm Scales......Page 421
4.4 Properties of Logarithms; Solving Exponential/Logarithmic Equations......Page 422
4.5 Applications from Business, Finance, and Science......Page 438
Technology Highlight: Exploring Compound Interest......Page 445
Summary and Concept Review......Page 451
Mixed Review......Page 455
Practice Test......Page 456
Calculator Exploration and Discovery: Investigating Logistic Equations......Page 457
Cumulative Review: Chapters 1–4......Page 459
Connections to Calculus: Properties of Logarithms; Area Functions; Expressions Involving e^x......Page 462
CHAPTER 5: An Introduction to Trigonometric Functions......Page 466
5.1 Angle Measure, Special Triangles, and Special Angles......Page 467
5.2 Unit Circles and the Trigonometry of Real Numbers......Page 481
5.3 Graphs of Sine and Cosine Functions; Cosecant and Secant Functions......Page 495
Technology Highlight: Exploring Amplitudes and Periods......Page 506
5.4 Graphs of Tangent and Cotangent Functions......Page 512
Technology Highlight: Zeroes, Asymptotes, and the Tangent/Cotangent Functions......Page 519
Mid-Chapter Check......Page 525
Reinforcing Basic Concepts: Trigonometry of the Real Numbers and the Wrapping Function......Page 526
5.5 Transformations and Applications of Trigonometric Graphs......Page 527
Technology Highlight: Locating Zeroes, Roots, and x-Intercepts......Page 535
5.6 The Trigonometry of Right Triangles......Page 540
5.7 Trigonometry and the Coordinate Plane......Page 553
Summary and Concept Review......Page 563
Mixed Review......Page 571
Practice Test......Page 573
Calculator Exploration and Discovery: Variable Amplitudes and Modeling the Tides......Page 575
Strengthening Core Skills: Standard Angles, Reference Angles, and the Trig Functions......Page 576
Cumulative Review: Chapters 1–5......Page 577
Connections to Calculus: Right Triangle Relationships; Algebraic Form and Polar Form......Page 580
CHAPTER 6: Trigonometric Identities, Inverses, and Equations......Page 584
6.1 Fundamental Identities and Families of Identities......Page 585
6.2 Constructing and Verifying Identities......Page 593
6.3 The Sum and Difference Identities......Page 599
6.4 The Double-Angle, Half-Angle, and Product-to-Sum Identities......Page 609
Mid-Chapter Check......Page 621
Reviewing Basic Concepts: Identities—Connections and Relationships......Page 622
6.5 The Inverse Trig Functions and Their Applications......Page 623
Technology Highlight: More on Inverse Functions......Page 633
6.6 Solving Basic Trig Equations......Page 640
Technology Highlight: Solving Equations Graphically......Page 646
6.7 General Trig Equations and Applications......Page 651
Summary and Concept Review......Page 660
Mixed Review......Page 664
Practice Test......Page 666
Calculator Exploration and Discovery: Seeing the Beats as the Beats Go On......Page 667
Strengthening Core Skills: Trigonometric Equations and Inequalities......Page 668
Cumulative Review: Chapters 1–6......Page 669
Connections to Calculus: Simplifying Expressions Using a Trigonometric Substitution; Trigonometric Identities and Equations......Page 671
CHAPTER 7: Applications of Trigonometry......Page 674
7.1 Oblique Triangles and the Law of Sines......Page 675
7.2 The Law of Cosines; the Area of a Triangle......Page 687
7.3 Vectors and Vector Diagrams......Page 699
Technology Highlight: Vector Components Given the Magnitude and the Angle ......Page 709
Reinforcing Basic Concepts: Scaled Drawings and the Laws of Sine and Cosine......Page 714
7.4 Vector Applications and the Dot Product......Page 715
7.5 Complex Numbers in Trigonometric Form......Page 728
7.6 De Moivre’s Theorem and the Theorem on nth Roots......Page 739
Summary and Concept Review......Page 746
Mixed Review......Page 750
Practice Test......Page 751
Calculator Exploration and Discovery: Investigating Projectile Motion......Page 753
Cumulative Review: Chapters 1–7......Page 754
Connections to Calculus: Trigonometry and Problem Solving; Vectors in Three Dimensions......Page 756
CHAPTER 8: Systems of Equations and Inequalities......Page 760
8.1 Linear Systems in Two Variables with Applications......Page 761
Technology Highlight: Solving Systems Graphically......Page 768
8.2 Linear Systems in Three Variables with Applications......Page 773
Technology Highlight: More on Parameterized Solutions......Page 780
8.3 Partial Fraction Decomposition......Page 784
8.4 Systems of Inequalities and Linear Programming......Page 796
Technology Highlight: Systems of Linear Inequalities......Page 804
Reinforcing Basic Concepts: Window Size and Graphing Technology......Page 809
8.5 Solving Linear Systems Using Matrices and Row Operations......Page 810
Technology Highlight: Solving Systems Using Matrices and Calculating Technology......Page 816
8.6 The Algebra of Matrices......Page 821
8.7 Solving Linear Systems Using Matrix Equations......Page 832
8.8 Applications of Matrices and Determinants: Cramer’s Rule, Geometry, and More......Page 847
Summary and Concept Review......Page 855
Mixed Review......Page 860
Practice Test......Page 861
Calculator Exploration and Discovery: Optimal Solutions and Linear Programming......Page 863
Strengthening Core Skills: Augmented Matrices and Matrix Inverses......Page 864
Cumulative Review: Chapters 1–8......Page 866
Connections to Calculus: More on Partial Fraction Decomposition; The Geometry of Vector and Determinants......Page 868
CHAPTER 9: Analytical Geometry and the Conic Sections......Page 872
9.1 A Brief Introduction to Analytic Geometry......Page 873
9.2 The Circle and the Ellipse......Page 880
9.3 The Hyperbola......Page 893
Technology Highlight: Studying Hyperbolas......Page 902
9.4 The Analytic Parabola......Page 907
Mid-Chapter Check......Page 915
9.5 Nonlinear Systems of Equations and Inequalities......Page 916
9.6 Polar Coordinates, Equations, and Graphs......Page 924
9.7 More on Conic Sections: Rotation of Axes and Polar Form......Page 937
Technology Highlight: Investigating the Eccentricity e......Page 948
9.8 Parametric Equations and Graphs......Page 954
Technology Highlight: Exploring Parametric Graphs......Page 960
Summary and Concept Review......Page 965
Mixed Review......Page 970
Practice Test......Page 971
Calculator Exploration and Discovery: Conic Rotations in Polar Form......Page 972
Strengthening Core Skills: Simplifying and Streamlining Computations for the Rotation of Axes......Page 973
Cumulative Review: Chapters 1–9......Page 975
Connections to Calculus: Polar Graphs and Instantaneous Rates of Change; Systems of Polar Equations......Page 976
CHAPTER 10: Additional Topics in Algebra......Page 980
10.1 Sequences and Series......Page 981
Technology Highlight: Studying Sequences and Series......Page 986
10.2 Arithmetic Sequences......Page 990
10.3 Geometric Sequences......Page 997
10.4 Mathematical Induction......Page 1007
Mid-Chapter Check......Page 1014
Reinforcing Basic Concepts: Applications of Summation......Page 1015
10.5 Counting Techniques......Page 1016
Technology Highlight: Calculating Permutations and Combinations......Page 1022
10.6 Introduction to Probability......Page 1028
Technology Highlight: Principles of Quick-Counting, Combinations, and Probability......Page 1033
10.7 The Binomial Theorem......Page 1040
Summary and Concept Review......Page 1048
Mixed Review......Page 1052
Practice Test......Page 1054
Calculator Exploration and Discovery: Infinite Series, Finite Results......Page 1055
Strengthening Core Skills: Probability, Quick Counting, and Card Games......Page 1056
Cumulative Review: Chapters 1–10......Page 1057
Connections to Calculus: Applications of Summation......Page 1060
CHAPTER 11: Bridges to Calculus–An Introduction to Limits......Page 1064
11.1 An Introduction to Limits Using Tables and Graphs......Page 1065
11.2 The Properties of Limits......Page 1075
Mid-Chapter Check......Page 1084
11.3 Continuity and More on Limits......Page 1085
11.4 Applications of Limits: Instantaneous Rates of Change and the Area Under a Curve......Page 1097
Summary and Concept Review......Page 1107
Mixed Review......Page 1110
Practice Test......Page 1111
Cumulative Review: Chapters 1–11......Page 1112
The Language, Notation, Numbers of Mathematics......Page 1114
Algebraic Expressions and the Properties of Real Numbers......Page 1121
Exponents, Scientific Notation, and a Review of Polynomials......Page 1127
Factoring Polynomials......Page 1137
Rational Expressions......Page 1144
Radicals and Rational Exponents......Page 1153
Appendix II: More on Synthetic Division......Page 1167
Appendix III: More on Matrices......Page 1169
Appendix IV: Deriving the Equation of a Conic......Page 1171
Appendix V: Selected Proofs......Page 1173
Appendix VI: Families of Polar Curves......Page 1176
Student Answer Appendix......Page 1179
Index......Page 1245