Algebra and Trigonometry with Modeling & Visualization,6th edition

• Gary K. Rockswold Minnesota State University, Mankato
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Algebra and Trigonometry with Modeling & Visualization doesnâ€™t just mention real-world examples; it teaches mathematical concepts through those applications. This approach allows you to learn the concepts in the context of the world you know, leading to better understanding and retention.

1. Introduction to Functions and Graphs

1.1 Numbers, Data, and Problem Solving

1.2 Visualizing and Graphing Data

Â Â Â Â Â Â Â  Â Â Â Â Â Â  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

Â Â Â Â Â Â Â  Â Â Â Â Â Â  Checking Basic Concepts for Sections 1.3 and 1.4

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Â Â Â Â Â Â Â  Â Â Â Â Â Â  Chapter 1 Summary

Â Â Â Â Â Â Â  Â Â Â Â Â Â  Chapter 1 Review Exercises

Â Â Â Â Â Â Â  Â Â Â Â Â Â  Chapter 1 Extended and Discovery Exercises

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2. Linear Functions and Equations

2.1 Equations of Lines

2.2 Linear Equations

Â Â Â Â Â Â Â  Â Â Â Â Â Â  Checking Basic Concepts for Sections 2.1 and 2.2

2.3 Linear Inequalities

2.4 More Modeling with Functions

Â Â Â Â Â Â Â  Â Â Â Â Â Â  Checking Basic Concepts for Sections 2.3 and 2.4

2.5 Absolute Value Equations and Inequalities

Â Â Â Â Â Â Â  Â Â Â Â Â Â  Checking Basic Concepts for Section 2.5

Â Â Â Â Â Â Â  Â Â Â Â Â Â  Chapter 2 Summary

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Â Â Â Â Â Â Â  Â Â Â Â Â Â  Chapter 2 Review Exercises

Â Â Â Â Â Â Â  Â Â Â Â Â Â  Chapter 2 Extended and Discovery Exercises

Â Â Â Â Â Â Â  Â Â Â Â Â Â  Chapters 1-2 Cumulative Review Exercises

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3.2 Quadratic Equations and Problem Solving

Â Â Â Â Â Â Â  Â Â Â Â Â Â  Checking Basic Concepts for Sections 3.1 and 3.2

3.3 Complex Numbers

Â Â Â Â Â Â Â  Â Â Â Â Â Â  Checking Basic Concepts for Sections 3.3 and 3.4

3.5 Transformations of Graphs

Â Â Â Â Â Â Â  Â Â Â Â Â Â  Checking Basic Concepts for Section 3.5

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Â Â Â Â Â Â Â  Â Â Â Â Â Â  Chapter 3 Summary

Â Â Â Â Â Â Â  Â Â Â Â Â Â  Chapter 3 Review Exercises

Â Â Â Â Â Â Â  Â Â Â Â Â Â  Chapter 3 Extended and Discovery Exercises

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4. More Nonlinear Functions and Equations

4.1 More Nonlinear Functions and Their Graphs

4.2 Polynomial Functions and Models

Â Â Â Â Â Â Â  Â Â Â Â Â Â  Checking Basic Concepts for Sections 4.1 and 4.2

4.3 Division of Polynomials

4.4 Real Zeros of Polynomial Functions

Â Â Â Â Â Â Â  Â Â Â Â Â Â  Checking Basic Concepts for Sections 4.3 and 4.4

4.5 The Fundamental Theorem of Algebra

4.6 Rational Functions and Models

Â Â Â Â Â Â Â  Â Â Â Â Â Â  Checking Basic Concepts for Sections 4.5 and 4.6

4.7 More Equations and Inequalities

4.8 Radical Equations and Power Functions

Â Â Â Â Â Â Â  Â Â Â Â Â Â  Checking Basic Concepts for Sections 4.7 and 4.8

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Â Â Â Â Â Â Â  Â Â Â Â Â Â  Chapter 4 Summary

Â Â Â Â Â Â Â  Â Â Â Â Â Â  Chapter 4 Review Exercises

Â Â Â Â Â Â Â  Â Â Â Â Â Â  Chapter 4 Extended and Discovery Exercises

Â Â Â Â Â Â Â  Â Â Â Â Â Â  Chapters 1-4 Cumulative Review Exercises

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5. Exponential and Logarithmic Functions

5.1 Combining Functions

5.2 Inverse Functions and Their Representations

Â Â Â Â Â Â Â  Â Â Â Â Â Â  Checking Basic Concepts for Sections 5.1 and 5.2

5.3 Exponential Functions and Models

5.4 Logarithmic Functions and Models

Â Â Â Â Â Â Â  Â Â Â Â Â Â  Checking Basic Concepts for Sections 5.3 and 5.4

5.5 Properties of Logarithms

5.6 Exponential and Logarithmic Equations

Â Â Â Â Â Â Â  Â Â Â Â Â Â  Checking Basic Concepts for Sections 5.5 and 5.6

5.7 Constructing Nonlinear Models

Â Â Â Â Â Â Â  Â Â Â Â Â Â  Checking Basic Concepts for Section 5.7

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Â Â Â Â Â Â Â  Â Â Â Â Â Â  Chapter 5 Summary

Â Â Â Â Â  Â Â Â Â Â Â Â Â  Chapter 5 Review Exercises

Â Â Â Â Â Â Â  Â Â Â Â Â Â  Chapter 5 Extended and Discovery Exercises

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6. Trigonometric Functions

6.1 Angles and Their Measure

6.2 Right Triangle Trigonometry

Â Â Â Â Â Â Â  Â Â Â Â Â Â  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

Â Â Â Â Â Â Â  Â Â Â Â Â Â  Checking Basic Concepts for Sections 6.3 and 6.4

6.5 Graphing Trigonometric Functions

6.6 Inverse Trigonometric Functions

Â Â Â Â Â Â Â  Â Â Â Â Â Â  Checking Basic Concepts for Sections 6.5 and 6.6

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Â Â Â Â Â Â Â  Â Â Â Â Â Â  Chapter 6 Summary

Â Â Â Â Â Â Â  Â Â Â Â Â Â  Chapter 6 Review Exercises

Â Â Â Â Â Â Â  Â Â Â Â Â Â  Chapter 6 Extended and Discovery Exercises

Â Â Â Â Â Â Â  Â Â Â Â Â Â  Chapters 1-6 Cumulative Review Exercises

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7. Trigonometric Identities and Equations

7.1 Fundamental Identities

7.2 Verifying Identities

Â Â Â Â Â Â Â  Â Â Â Â Â Â  Checking Basic Concepts for Sections 7.1 and 7.2

7.3 Trigonometric Equations

7.4 Sum and Difference Identities

Â Â Â Â Â Â Â  Â Â Â Â Â Â  Checking Basic Concepts for Sections 7.3 and 7.4

7.5 Multiple-Angle Identities

Â Â Â Â Â Â Â  Â Â Â Â Â Â  Checking Basic Concepts for Section 7.5

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Â Â Â Â Â Â Â  Â Â Â Â Â Â  Chapter 7 Summary

Â Â Â Â Â Â Â  Â Â Â Â Â Â  Chapter 7 Review Exercises

Â Â Â Â Â Â Â  Â Â Â Â Â Â  Chapter 7 Extended and Discovery Exercises

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8. Further Topics in Trigonometry

8.1 Law of Sines

8.2 Law of Cosines

Â Â Â Â Â Â Â  Â Â Â Â Â Â  Checking Basic Concepts for Sections 8.1 and 8.2

8.3 Vectors

8.4 Parametric Equations

Â Â Â Â Â Â Â  Â Â Â Â Â Â  Checking Basic Concepts for Sections 8.3 and 8.4

8.5 Polar Equations

8.6 Trigonometric Form and Roots of Complex Numbers

Â Â Â Â Â Â Â  Â Â Â Â Â Â  Checking Basic Concepts for Sections 8.5 and 8.6

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Â Â Â Â Â Â Â  Â Â Â Â Â Â  Chapter 8 Summary

Â Â Â Â Â Â Â  Â Â Â Â Â Â  Chapter 8 Review Exercises

Â Â Â Â Â Â Â  Â Â Â Â Â Â  Chapter 8 Extended and Discovery Exercises

Â Â Â Â Â Â Â  Â Â Â Â Â Â  Chapters 1-8 Cumulative Review Exercises

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9. Systems of Equations and Inequalities

9.1 Functions and Systems of Equations in Two Variables

9.2 Systems of Inequalities in Two Variables

Â Â Â Â Â Â Â  Â Â Â Â Â Â  Checking Basic Concepts for Sections 9.1 and 9.2

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9.3 Systems of Linear Equations in Three Variables

9.4 Solutions to Linear Systems Using Matrices

Â Â Â Â Â Â Â  Â Â Â Â Â Â  Checking Basic Concepts for Sections 9.3 and 9.4

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9.5 Properties and Applications of Matrices

9.6 Inverses of Matrices

Â Â Â Â Â Â Â  Â Â Â Â Â Â  Checking Basic Concepts for Sections 9.5 and 9.6

9.7 Determinants

Â Â Â Â Â Â Â  Â Â Â Â Â Â  Checking Basic Concepts for Section 9.7

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Â Â Â Â Â Â Â  Â Â Â Â Â Â  Chapter 9 Summary

Â Â Â Â Â Â Â  Â Â Â Â Â Â  Chapter 9 Review Exercises

Â Â Â Â Â Â Â  Â Â Â Â Â Â  Chapter 9 Extended and Discovery Exercises

Â Â Â Â Â Â Â  Â Â Â Â Â Â  Chapters 1-9 Cumulative Review Exercises

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10. Conic Sections

10.1 Parabolas

10.2 Ellipses

Â Â Â Â Â Â Â  Â Â Â Â Â Â  Checking Basic Concepts for Sections 10.1 and 10.2

10.3 Hyperbolas

Â Â Â Â Â Â Â  Â Â Â Â Â Â  Checking Basic Concepts for Section 10.3

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Â Â Â Â Â Â Â  Â Â Â Â Â Â  Chapter 10 Summary

Â Â Â Â Â Â Â  Â Â Â Â Â Â  Chapter 10 Review Exercises

Â Â Â Â Â Â Â  Â Â Â Â Â Â  Chapter 10 Extended and Discovery Exercises

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11. Further Topics in Algebra

11.1 Sequences

11.2 Series

Â Â Â Â Â Â Â  Â Â Â Â Â Â  Checking Basic Concepts for Sections 11.1 and 11.2

11.3 Counting

11.4 The Binomial Theorem

Â Â Â Â Â Â Â  Â Â Â Â Â Â  Checking Basic Concepts for Sections 11.3 and 11.4

11.5 Mathematical Induction

11.6 Probability

Â Â Â Â Â Â Â  Â Â Â Â Â Â  Checking Basic Concepts for Sections 11.5 and 11.6

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Â Â Â Â Â Â Â  Â Â Â Â Â Â  Chapter 11 Summary

Â Â Â Â Â Â Â  Â Â Â Â Â Â  Chapter 11 Review Exercises

Â Â Â Â Â Â Â  Â Â Â Â Â Â  Chapter 11 Extended and Discovery Exercises

Â Â Â Â Â Â Â  Â Â Â Â Â Â  Chapters 1-11 Cumulative Review Exercises

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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

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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

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Bibliography