Precalculus with Modeling & Visualization

By connecting applications, modeling, and visualization, Gary Rockswold motivates students to learn mathematics in the context of their experiences. In order to both learn and retain the material, students must see a connection between the concepts and their real lives. In this new edition, connections are taken to a new level with “See the Concept” features, where students make important connections through detailed visualizations that deepen understanding.

1. Introduction to Functions and Graphs

1.1 Numbers, Data, and Problem Solving

1.2 Visualizing and Graphing Data

            Checking Basic Concepts for Sections 1.1 and 1.2

1.3 Functions and Their Representations

1.4 Types of Functions and Their Rates of Change

            Checking Basic Concepts for Sections 1.3 and 1.4

            Chapter 1 Summary

            Chapter 1 Review Exercises

            Chapter 1 Extended and Discovery Exercises

2. Linear Functions and Equations

2.1 Equations of Lines

2.2 Linear Equations

            Checking Basic Concepts for Sections 2.1 and 2.2

2.3 Linear Inequalities

2.4 More Modeling with Functions

            Checking Basic Concepts for Sections 2.3 and 2.4

2.5 Absolute Value Equations and Inequalities

            Checking Basic Concepts for Section 2.5

            Chapter 2 Summary

            Chapter 2 Review Exercises

            Chapter 2 Extended and Discovery Exercises

            Chapters 1-2 Cumulative Review Exercises

3. Quadratic Functions and Equations

3.1 Quadratic Functions and Models

3.2 Quadratic Equations and Problem Solving

            Checking Basic Concepts for Sections 3.1 and 3.2

3.3 Complex Numbers

3.4 Quadratic Inequalities

            Checking Basic Concepts for Sections 3.3 and 3.4

3.5 Transformations of Graphs

            Checking Basic Concepts for Section 3.5

            Chapter 3 Summary

            Chapter 3 Review Exercises

            Chapter 3 Extended and Discovery Exercises

4. More Nonlinear Functions and Equations

4.1 More Nonlinear Functions and Their Graphs

4.2 Polynomial Functions and Models

            Checking Basic Concepts for Sections 4.1 and 4.2

4.3 Division of Polynomials

4.4 Real Zeros of Polynomial Functions

            Checking Basic Concepts for Sections 4.3 and 4.4

4.5 The Fundamental Theorem of Algebra

4.6 Rational Functions and Models

            Checking Basic Concepts for Sections 4.5 and 4.6

4.7 More Equations and Inequalities

4.8 Radical Equations and Power Functions

            Checking Basic Concepts for Sections 4.7 and 4.8

            Chapter 4 Summary

            Chapter 4 Review Exercises

            Chapter 4 Extended and Discovery Exercises

            Chapters 1-4 Cumulative Review Exercises

5. Exponential and Logarithmic Functions

5.1 Combining Functions

5.2 Inverse Functions and Their Representations

            Checking Basic Concepts for Sections 5.1 and 5.2

5.3 Exponential Functions and Models

5.4 Logarithmic Functions and Models

            Checking Basic Concepts for Sections 5.3 and 5.4

5.5 Properties of Logarithms

5.6 Exponential and Logarithmic Equations

            Checking Basic Concepts for Sections 5.5 and 5.6

5.7 Constructing Nonlinear Models

            Checking Basic Concepts for Section 5.7

            Chapter 5 Summary

            Chapter 5 Review Exercises

            Chapter 5 Extended and Discovery Exercises

6. Trigonometric Functions

6.1 Angles and Their Measure

6.2 Right Triangle Trigonometry

            Checking Basic Concepts for Sections 6.1 and 6.2

6.3 The Sine and Cosine Functions and Their Graphs

6.4 Other Trigonometric Functions and Their Graphs

            Checking Basic Concepts for Sections 6.3 and 6.4

6.5 Graphing Trigonometric Functions

6.6 Inverse Trigonometric Functions

            Checking Basic Concepts for Sections 6.5 and 6.6

            Chapter 6 Summary

            Chapter 6 Review Exercises

            Chapter 6 Extended and Discovery Exercises

            Chapters 1-6 Cumulative Review Exercises

7. Trigonometric Identities and Equations

7.1 Fundamental Identities

7.2 Verifying Identities

            Checking Basic Concepts for Sections 7.1 and 7.2

7.3 Trigonometric Equations

7.4 Sum and Difference Identities

            Checking Basic Concepts for Sections 7.3 and 7.4

7.5 Multiple-Angle Identities

            Checking Basic Concepts for Section 7.5

            Chapter 7 Summary

            Chapter 7 Review Exercises

            Chapter 7 Extended and Discovery Exercises

8. Further Topics in Trigonometry

8.1 Law of Sines

8.2 Law of Cosines

            Checking Basic Concepts for Sections 8.1 and 8.2

8.3 Vectors

8.4 Parametric Equations

            Checking Basic Concepts for Sections 8.3 and 8.4

8.5 Polar Equations

8.6 Trigonometric Form and Roots of Complex Numbers

            Checking Basic Concepts for Sections 8.5 and 8.6

            Chapter 8 Summary

            Chapter 8 Review Exercises

            Chapter 8 Extended and Discovery Exercises

            Chapters 1-8 Cumulative Review Exercises

9. Systems of Equations and Inequalities

9.1 Functions and Systems of Equations in Two Variables

9.2 Systems of Inequalities in Two Variables

            Checking Basic Concepts for Sections 9.1 and 9.2

9.3 Systems of Linear Equations in Three Variables

9.4 Solutions to Linear Systems Using Matrices

            Checking Basic Concepts for Sections 9.3 and 9.4

9.5 Properties and Applications of Matrices

9.6 Inverses of Matrices

            Checking Basic Concepts for Sections 9.5 and 9.6

9.7 Determinants

            Checking Basic Concepts for Section 9.7

            Chapter 9 Summary

            Chapter 9 Review Exercises

            Chapter 9 Extended and Discovery Exercises

            Chapters 1-9 Cumulative Review Exercises

10. Conic Sections

10.1 Parabolas

10.2 Ellipses

            Checking Basic Concepts for Sections 10.1 and 10.2

10.3 Hyperbolas

            Checking Basic Concepts for Section 10.3

            Chapter 10 Summary

            Chapter 10 Review Exercises

            Chapter 10 Extended and Discovery Exercises

11. Further Topics in Algebra

11.1 Sequences

11.2 Series

            Checking Basic Concepts for Sections 11.1 and 11.2

11.3 Counting

11.4 The Binomial Theorem

            Checking Basic Concepts for Sections 11.3 and 11.4

11.5 Mathematical Induction

11.6 Probability

            Checking Basic Concepts for Sections 11.5 and 11.6

            Chapter 11 Summary

            Chapter 11 Review Exercises

            Chapter 11 Extended and Discovery Exercises

            Chapters 1-11 Cumulative Review Exercises

R. 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

Appendix D: Percent Change and Exponential Functions

Appendix E: Rotation of Axes

Bibliography

Answers to Selected Exercises

Photo Credits

Index of Applications

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