Precalculus with Modeling and Visualization

1. Introduction to Functions and Graphs

1.1 Numbers, Data, and Problem Solving

1.2 Visualizing and Graphing Data

1.3 Functions and Their Representations

1.4 Types of Functions

1.5 Functions and Their Rates of Change



2. Linear Functions and Equations

2.1 Linear Functions and Models

2.2 Equations of Lines

2.3 Linear Equations

2.4 Linear Inequalities

2.5 Absolute Value Equations and Inequalities



3. Quadratic Functions and Equations

3.1 Quadratic Functions and Models

3.2 Quadratic Equations and Problem Solving

3.3 Complex Numbers

3.4 Quadratic Inequalities

3.5 Transformations of Graphs



4. More Nonlinear Functions and Equations

4.1 More Nonlinear Functions and Their Graphs

4.2 Polynomial Functions and Models

4.3 Division of Polynomials

4.4 Real Zeros of Polynomial Functions

4.5 The Fundamental Theorem of Algebra

4.6 Rational Functions and Models

4.7 More Equations and Inequalities

4.8 Radical Equations and Power Functions



5. Exponential and Logarithmic Functions

5.1 Combining Functions

5.2 Inverse Functions and Their Representations

5.3 Exponential Functions and Models

5.4 Logarithmic Functions and Models

5.5 Properties of Logarithms

5.6 Exponential and Logarithmic Equations

5.7 Constructing Nonlinear Models



6. Trigonometric Functions

6.1 Angles and Their Measure

6.2 Right Triangle Trigonometry

6.3 The Sine and Cosine Functions and Their Graphs

6.4 Other Trigonometric Functions and Their Graphs

6.5 Graphing Trigonometric Functions

6.6 Inverse Trigonometric Functions



7. Trigonometric Identities and Equations

7.1 Fundamental Identities

7.2 Verifying Identities

7.3 Trigonometric Equations

7.4 Sum and Difference Identities

7.5 Multiple-Angle Identities



8. Further Topics in Trigonometry

8.1 Law of Sines

8.2 Law of Cosines

8.3 Vectors

8.4 Parametric Equations

8.5 Polar Equations

8.6 Trigonometric Form and Roots of Complex Numbers



9. Systems of Equations and Inequalities

9.1 Functions and Systems of Equations in Two Variables

9.2 Systems of Inequalities in Two Variables

9.3 Systems of Linear Equations in Three Variables

9.4 Solutions to Linear Systems Using Matrices

9.5 Properties and Applications of Matrices

9.6 Inverses of Matrices

9.7 Determinants



10. Conic Sections

10.1 Parabolas

10.2 Ellipses

10.3 Hyperbolas



11. Further Topics in Algebra

11.1 Sequences

11.2 Series

11.3 Counting

11.4 The Binomial Theorem

11.5 Mathematical Induction

11.6 Probability



Reference: Basic Concepts from Algebra and Geometry

R.1 Formulas from Geometry

R.2 Integer Exponents

R.3 Polynomial Expressions

R.4 Factoring Polynomials

R.5 Rational Expressions

R.6 Radical Notation and Rational Exponents

R.7 Radical Expressions



Appendix A: Using the Graphing Calculator

Appendix B: A Library of Functions

Appendix C: Partial Fractions



Bibliography

Answers to Selected Exercises

Index of Applications

Index