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Table of Contents

R. Review

R.1 Real Numbers

R.2 Algebra Essentials

R.3 Geometry Essentials

R.4 Polynomials

R.5 Factoring Polynomials

R.6 Synthetic Division

R.7 Rational Expressions

R.8 nth Roots; Rational Exponents

1. Graphs, Equations, and Inequalities

1.1 The Distance and Midpoint Formulas; Graphing Utilities; Introduction to Graphing Equations

1.2 Solving Equations Using a Graphing Utility; Linear and Rational Equations

1.3 Quadratic Equations

1.4 Complex Numbers; Quadratic Equations in the Complex Number System

1.5 Radical Equations; Equations Quadratic in Form; Absolute Value Equations; FactorTable Equations

1.6 Problem Solving: Interest, Mixture, Uniform Motion, Constant Rate Jobs

1.7 Solving Inequalities

Chapter Review

Chapter Test

Cumulative Review

Chapter Projects

2. Graphs

2.1 Intercepts; Symmetry; Graphing Key Equations

2.2 Lines

2.3 Circles

2.4 Variation

Chapter Review

Chapter Test

Cumulative Review

Chapter Projects

3. Functions and Their Graphs

3.1 Functions

3.2 The Graph of a Function

3.3 Properties of Functions

3.4 Library of Functions; Piecewise-defined Functions

3.5 Graphing Techniques: Transformations

3.6 Mathematical Models: Building Functions

Chapter Review

Chapter Test

Cumulative Review

Chapter Projects

4. Linear and Quadratic Functions

4.1 Linear Functions, Their Properties, and Linear Models

4.2 Building Linear Models from Data

4.3 Quadratic Functions and Their Properties

4.4 Building Quadratic Models from Verbal Descriptions and Data

4.5 Inequalities Involving Quadratic Functions

Chapter Review

Chapter Test

Cumulative Review

Chapter Projects

5. Polynomial and Rational Functions

5.1 Polynomial Functions and Models

5.2 The Real Zeros of a Polynomial Function

5.3 Properties of Rational Functions

5.4 The Graph of a Rational Function

5.5 Polynomial and Rational Inequalities

5.6 Complex Zeros; Fundamental Theorem of Algebra

Chapter Review

Chapter Test

Cumulative Review

Chapter Projects

6. Exponential and Logarithmic Functions

6.1 Composite Functions

6.2 One-to-One Functions; Inverse Functions

6.3 Exponential Functions

6.4 Logarithmic Functions

6.5 Properties of Logarithms

6.6 Logarithmic and Exponential Equations

6.7 Financial Models

6.8 Exponential Growth and Decay Models; Newton’s Law; Logistic Growth and Decay Models

6.9 Building Exponential, Logarithmic, and Logistic Models from Data

Chapter Review

Chapter Test

Cumulative Review

Chapter Projects

7. Trigonometric Functions

7.1 Angles and Their Measure

7.2 Right Triangle Trigonometry

7.3 Computing the Values of Trigonometric Functions of Acute Angles

7.4 Trigonometric Functions of Any Angle

7.5 Unit Circle Approach; Properties of the Trigonometric Functions

7.6 Graphs of the Sine and Cosine Functions

7.7 Graphs of the Tangent, Cotangent, Cosecant, and Secant Functions

7.8 Phase Shift; Building Sinusoidal Models

Chapter Review

Chapter Test

Cumulative Review

Chapter Projects

8. Analytic Trigonometry

8.1 The Inverse Sine, Cosine, and Tangent Functions

8.2 The Inverse Trigonometric Functions (Continued)

8.3 Trigonometric Equations

8.4 Trigonometric Identities

8.5 Sum and Difference Formulas

8.6 Double-angle and Half-angle Formulas

8.7 Product-to-Sum and Sum-to-Product Formulas

Chapter Review

Chapter Test

Cumulative Review

Chapter Projects

9. Applications of Trigonometric Functions

9.1 Applications Involving Right Triangles

9.2 The Law of Sines

9.3 The Law of Cosines

9.4 Area of a Triangle

9.5 Simple Harmonic Motion; Damped Motion; Combining Waves

Chapter Review

Chapter Test

Cumulative Review

Chapter Projects

10. Polar Coordinates; Vectors

10.1 Polar Coordinates

10.2 Polar Equations and Graphs

10.3 The Complex Plane; DeMoivre’s Theorem

10.4 Vectors

10.5 The Dot Product

Chapter Review

Chapter Test

Cumulative Review

Chapter Projects

11. Analytic Geometry

11.1 Conics

11.2 The Parabola

11.3 The Ellipse

11.4 The Hyperbola

11.5 Rotation of Axes; General Form of a Conic

11.6 Polar Equations of Conics

11.7 Plane Curves and Parametric Equations

Chapter Review

Chapter Test

Cumulative Review

Chapter Projects

12. Systems of Equations and Inequalities

12.1 Systems of Linear Equations: Substitution and Elimination

12.2 Systems of Linear Equations: Matrices

12.3 Systems of Linear Equations: Determinants

12.4 Matrix Algebra

12.5 Partial Fraction Decomposition

12.6 Systems of Nonlinear Equations

12.7 Systems of Inequalities

12.8 Linear Programming

Chapter Review

Chapter Test

Cumulative Review

Chapter Projects

13. Sequences; Induction; the Binomial Theorem

13.1 Sequences

13.2 Arithmetic Sequences

13.3 Geometric Sequences; Geometric Series

13.4 Mathematical Induction

13.5 The Binomial Theorem

Chapter Review

Chapter Test

Cumulative Review

Chapter Projects

14. Counting and Probability

14.1 Counting

14.2 Permutations and Combinations

14.3 Probability

Chapter Review

Chapter Test

Cumulative Review

Chapter Projects

Answers

Index