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Contents
F. Foundations: A Prelude to Functions
F.1 The Distance and Midpoint Formulas
F.2 Graphs of Equations in Two Variables; Intercepts; Symmetry
F.3 Lines
F.4 Circles
1. Functions and Their Graphs
1.1 Functions
1.2 The Graph of a Function
1.3 Properties of Functions
1.4 Library of Functions; Piecewise-defined Functions
1.5 Graphing Techniques: Transformations
1.6 Mathematical Models: Constructing Functions
1.7 Building Mathematical Models Using Variation
Chapter Review
Chapter Test
Chapter Projects
2. Linear and Quadratic Functions
2.1 Properties of Linear Functions and Linear Models
2.2 Building Linear Models from Data
2.3 Quadratic Functions and Their Zeros
2.4 Properties of Quadratic Functions
2.5 Inequalities Involving Quadratic Functions
2.6 Building Quadratic Models from Verbal Descriptions and from Data
2.7 Complex Zeros of a Quadratic Function
2.8 Equations and Inequalities Involving the Absolute Value Function
Chapter Review
Chapter Test
Chapter Projects
Cumulative Review
3. Polynomial and Rational Functions
3.1 Polynomial Functions and Models
3.2 The Real Zeros of a Polynomial Function
3.3 Complex Zeros; Fundamental Theorem of Algebra
3.4 Properties of Rational Functions
3.5 The Graph of a Rational Function
3.6 Polynomial and Rational Inequalities
Chapter Review
Chapter Test
Chapter Projects
Cumulative Review
4. Exponential and Logarithmic Functions
4.1 Composite Functions
4.2 One-to-One Functions; Inverse Functions
4.3 Exponential Functions
4.4 Logarithmic Functions
4.5 Properties of Logarithms
4.6 Logarithmic and Exponential Equations
4.7 Compound Interest
4.8 Exponential Growth and Decay; Newton's Law; Logistic Growth and Decay
4.9 Building Exponential, Logarithmic, and Logistic Functions from Data
Chapter Review
Chapter Test
Chapter Projects
Cumulative Review
5. Trigonometric Functions
5.1 Angles and Their Measure
5.2 Right Triangle Trigonometry
5.3 Computing the Values of Trigonometric Functions of Acute Angles
5.4 Trigonometric Functions of Any Angle
5.5 Unit Circle Approach; Properties of the Trigonometric Functions
5.6 Graphs of the Sine and Cosine Functions
5.7 Graphs of the Tangent, Cotangent, Cosecant, and Secant Functions
5.8 Phase Shift; Sinusoidal Curve Fitting
Chapter Review
Chapter Test
Chapter Projects
Cumulative Review
6. Analytic Trigonometry
6.1 The Inverse Sine, Cosine, and Tangent Functions
6.2 The Inverse Trigonometric Functions (Continued)
6.3 Trigonometric Equations
6.4 Trigonometric Identities
6.5 Sum and Difference Formulas
6.6 Double-angle and Half-angle Formulas
6.7 Product-to-Sum and Sum-to-Product Formulas
Chapter Review
Chapter Test
Chapter Projects
Cumulative Review
7. Applications of Trigonometric Functions
7.1 Right Triangle Trigonometry; Applications Involving Right Triangles
7.2 The Law of Sines
7.3 The Law of Cosines
7.4 Area of a Triangle
7.5 Simple Harmonic Motion; Damped Motion; Combining Waves
Chapter Review
Chapter Test
Chapter Projects
Cumulative Review
8. Polar Coordinates; Vectors
8.1 Polar Coordinates
8.2 Polar Equations and Graphs
8.3 The Complex Plane; DeMoivre's Theorem
8.4 Vectors
8.5 The Dot Product
8.6 Vectors in Space
8.7 The Cross Product
Chapter Review
Chapter Test
Chapter Projects
Cumulative Review
9. Analytic Geometry
9.1 Conics
9.2 The Parabola
9.3 The Ellipse
9.4 The Hyperbola
9.5 Rotation of Axes; General Form of a Conic
9.6 Polar Equations of Conics
9.7 Plane Curves and Parametric Equations
Chapter Review
Chapter Test
Chapter Projects
Cumulative Review
10. Systems of Equations and Inequalities
10.1 Systems of Linear Equations: Substitution and Elimination
10.2 Systems of Linear Equations: Matrices
10.3 Systems of Linear Equations: Determinants
10.4 Matrix Algebra
10.5 Partial Fraction Decomposition
10.6 Systems of Nonlinear Equations
10.7 Systems of Inequalities
10.8 Linear Programming
Chapter Review
Chapter Test
Chapter Projects
Cumulative Review
11. Sequences; Induction; the Binomial Theorem
11.1 Sequences
11.2 Arithmetic Sequences
11.3 Geometric Sequences; Geometric Series
11.4 Mathematical Induction
11.5 The Binomial Theorem
Chapter Review
Chapter Test
Chapter Projects
Cumulative Review
12. Counting and Probability
12.1 Counting
12.2 Permutations and Combinations
12.3 Probability
Chapter Review
Chapter Test
Chapter Projects
Cumulative Review
13. A Preview of Calculus: The Limit, Derivative, and Integral of a Function
13.1 Finding Limits Using Tables and Graphs
13.2 Algebra Techniques for Finding Limits
13.3 One-sided Limits; Continuous Functions
13.4 The Tangent Problem; The Derivative
13.5 The Area Problem; The Integral
Chapter Review
Chapter Test
Chapter Projects
Appendix A. Review
A.1 Algebra Essentials
A.2 Geometry Essentials
A.3 Polynomials
A.4 Factoring Polynomials
A.5 Synthetic Division
A.6 Rational Expressions
A.7 nth Roots; Rational Exponents
A.8 Solving Equations
A.9 Problem Solving: Interest, Mixture, Uniform Motion, Constant Rate Jobs
A.10 Interval Notation; Solving Inequalities
A.11 Complex Numbers
Appendix B. Graphing Utilities
B.1 The Viewing Rectangle
B.2 Using a Graphing Utility to Graph Equations
B.3 Using a Graphing Utility to Locate Intercepts and Check for Symmetry
B.4 Using a Graphing Utility to Solve Equations
B.5 Square Screens
B.6 Using a Graphing Utility to Graph Inequalities
B.7 Using a Graphing Utility to Solve Systems of Linear Equations
B.8 Using a Graphing Utility to Graph a Polar Equation
B.9 Using a Graphing Utility to Graph Parametric Equations
Answers
Index
