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by Margaret Lial, John Hornsby and David Schneider

Edition: 3RD 05Copyright: 2005

Publisher: Addison-Wesley Longman, Inc.

Published: 2005

International: No

Margaret Lial, John Hornsby and David Schneider

Edition: 3RD 05
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Focusing on helping students to develop both the conceptual understanding and the analytical skills necessary to experience success in mathematics, we present each mathematical topic in this text using a carefully developed learning system to actively engage students in the learning process. We have tried to address the diverse needs of today's students through a more open design, updated figures and graphs, helpful features, careful explanations of topics, and a comprehensive package of supplements and study aids. Students will benefit from the text's student-oriented approach. We believe instructors will particularly welcome the new Annotated Instructor's Edition, which provides answers in the margin to almost all exercises, plus helpful Teaching Tips.

**Features **

- Real-Life Applications We are always on the lookout for interesting data to use in real-life applications. As a result, we have updated or incorporated many new or examples and exercises from fields such as business, pop culture, sports, life sciences, and environmental studies that show the relevance of algebra to daily life. Applications that feature mathematical modeling are labeled with a Modeling head. All applications are titled, and a comprehensive Index of Applications is included at the back of the text.
- Use of Technology As in the previous edition, we have integrated the use of graphing calculators where appropriate, although graphing technology is not a central feature of this text. We continue to stress that graphing calculators are an aid to understanding and that students must master the underlying mathematical concepts first. We have included graphing calculator solutions for selected examples and continue to mark all graphing calculator notes and exercises that use graphing calculators with an icon for easy identification and added flexibility. This graphing calculator material is optional and can be omitted without loss of continuity.
- Cautions and Notes We often give students warnings of common errors and emphasize important ideas in Caution and Note comments that appear throughout the exposition.
- Looking Ahead to Calculus These margin notes offer glimpses of how the algebraic topics currently being studied are used in calculus.
- Connections This boxed feature provides connections to the real world or to other mathematical concepts, historical background, and thought-provoking questions for writing, class discussion, or group work.
- Relating Concepts Exercises Appearing in selected exercise sets, these sets of problems help students tie together topics and develop problem-solving skills as they compare and contrast ideas, identify and describe patterns, and extend concepts to new situations. These exercises make great collaborative activities for pairs or small groups of students.

**New To This Edition **

- Examples We have added even more examples in this edition. Step-by-step solutions to examples are now easily identified using a Solution head. We have carefully polished all solutions and incorporated more side comments and explanations, including helpful section references to previously-covered material. Selected examples continue to provide graphing calculator solutions alongside traditional algebraic solutions. The graphing calculator solutions can be easily omitted if desired.
- Now try Exercises To actively engage students in the learning process, each example now concludes with a reference to one or more parallel, odd-numbered exercises from the corresponding exercise set. In this way, students are able to immediately apply and reinforce the concepts and skills presented in the examples.
- Exercise Sets We have taken special care to respond to the suggestions of users and reviewers and have added many new exercises to this edition based on their feedback. As a result, the text includes more problems than ever to provide students with ample opportunities to practice, apply, connect, and extend concepts and skills. We have included writing exercises and optional graphing calculator problems as well as multiple-choice, matching, true/false, and completion problems. Concept Check problems, which focus on mathematical thinking and conceptual understanding, were well received in the previous edition and have been expanded in this edition.
- Solutions to Selected Exercises Exercise numbers enclosed in a blue circle indicate that a complete solution for the problem is included at the back of the text. These new solutions are given for selected exercises that extend the skills and concepts presented in the section examples. There are approximately 3 to 5 per section.
- Summary Exercises These new sets of in-chapter exercises in most chapters provide students with the all-important mixed review problems they need to synthesize concepts and select appropriate solution methods.
- Function Boxes Beginning in Chapter 2, functions are a unifying theme throughout the remainder of the text. To that end, special function boxes offer a comprehensive, visual introduction to each class of function and also serve as an excellent resource for student reference and review throughout the course. Each function box includes a table of values alongside traditional and calculator graphs, as well as the domain, range, and other specific information about the function.
- Chapter Reviews Each Chapter ends with an expanded Summary, featuring a section-by-section list of Key Terms, New Symbols, and a Quick Review of important Concepts, presented alongside corresponding all-new Examples. A comprehensive set of Review Excercises and a Chapter Test are also provided.
- Quantitative Reasoning Now appearing at the end of each chapter, these problems enable students to apply algebraic concepts to real-life situations, such as financial planning for retirement or determining the value of a college education. A photo highlights each problem.
- Glossary As an additional student study aid, a comprehensive glossary of key terms from throughout the text is provided at the back of the book.
- New Annotated Instructor's Edition --This special edition of the text provides answers to almost all text exercises in color on the page that the exercise appears. This provides the instructor with immediate access to answers without searching the back of the book.

**R. Review of Basic Concepts. **

Real Numbers and Their Properties.

Order and Absolute Value.

Polynomials.

Factoring Polynomials.

Rational Expressions.

Rational Exponents.

Radical Expressions.

**1. Equations and Inequalities. **

Linear Equations.

Applications and Modeling with Linear Equations.

Complex Numbers.

Quadratic Equations.

Applications and Modeling with Quadratic Equations.

Other Types of Equations.

Inequalities.

Absolute Value Equations and Inequalities.

**2. Graphs and Functions. **

Graphs of Equations.

Functions.

Linear Functions.

Equations of Lines; Curve Fitting.

Graphs of Basic Functions.

Graphing Techniques.

Function Operations and Composition.

**3. Polynomial and Rational Functions. **

Quadratic Functions and Models.

Synthetic Division.

Zeros of Polynomial Functions.

Polynomial Functions: Graphs, Applications, and Models.

Rational Functions: Graphs, Applications, and Models.

Variation.

**4. Exponential and Logarithmic Functions. **

Inverse Functions.

Exponential Functions.

Logarithmic Functions.

Evaluating Logarithms and the Change-of-Base Theorem.

Exponential and Logarithmic Equations.

Applications and Models of Exponential Growth and Decay.

**5. Trigonometric Functions. **

Angles.

Trigonometric Functions.

Evaluating Trigonometric Functions.

Solving Right Triangles.

**6. The Circular Functions and Their Graphs. **

Radian Measure.

The Unit Circle and Circular Functions.

Graphs of the Sine and Cosine Functions.

Graphs of the Other Circular Functions.

Harmonic Motion.

**7. Trigonometric Identities and Equations. **

Fundamental Identities.

Verifying Trigonometric Identities.

Sum and Difference Identities.

Double-Angle Identities and Half-Angle Identities.

Inverse Circular Functions.

Trigonometric Equations.

Equations Involving Inverse Trigonometric Functions.

**8. Applications of Trigonometry. **

The Law of Sines.

The Law of Cosines.

Vectors, Operations, and the Dot Product.

Applications of Vectors.

Trigonometric (Polar) Form of Complex Numbers; Products and Quotients.

DeMoivre's Theorem; Powers and Roots of Complex Numbers.

Polar Equations and Graphs.

Parametric Equations, Graphs, and Applications.

**9. Systems and Matrices. **

Systems of Linear Equations.

Matrix Solution of Linear Systems.

Determinant Solution of Linear Systems.

Partial Fractions.

Nonlinear Systems of Equations.

Systems of Inequalities and Linear Programming.

Properties of Matrices.

Matrix Inverses.

**10. Analytic Geometry. **

Parabolas.

Ellipses.

Hyperbolas.

Summary of the Conic Sections.

**11. Further Topics in Algebra. **

Sequences and Series.

Arithmetic Sequences and Series.

Geometric Sequences and Series.

The Binomial Theorem.

Mathematical Induction.

Counting Theory.

Basics of Probability.

Appendix A. Polar Form of Conic Sections.

Appendix B. Rotation of Axes.

Glossary.

Solutions to Selected Exercises.

Answers to Selected Exercises.

Index of Applications.

Index.

Appendix C: Geometry Formulas.

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Summary

Focusing on helping students to develop both the conceptual understanding and the analytical skills necessary to experience success in mathematics, we present each mathematical topic in this text using a carefully developed learning system to actively engage students in the learning process. We have tried to address the diverse needs of today's students through a more open design, updated figures and graphs, helpful features, careful explanations of topics, and a comprehensive package of supplements and study aids. Students will benefit from the text's student-oriented approach. We believe instructors will particularly welcome the new Annotated Instructor's Edition, which provides answers in the margin to almost all exercises, plus helpful Teaching Tips.

**Features **

- Real-Life Applications We are always on the lookout for interesting data to use in real-life applications. As a result, we have updated or incorporated many new or examples and exercises from fields such as business, pop culture, sports, life sciences, and environmental studies that show the relevance of algebra to daily life. Applications that feature mathematical modeling are labeled with a Modeling head. All applications are titled, and a comprehensive Index of Applications is included at the back of the text.
- Use of Technology As in the previous edition, we have integrated the use of graphing calculators where appropriate, although graphing technology is not a central feature of this text. We continue to stress that graphing calculators are an aid to understanding and that students must master the underlying mathematical concepts first. We have included graphing calculator solutions for selected examples and continue to mark all graphing calculator notes and exercises that use graphing calculators with an icon for easy identification and added flexibility. This graphing calculator material is optional and can be omitted without loss of continuity.
- Cautions and Notes We often give students warnings of common errors and emphasize important ideas in Caution and Note comments that appear throughout the exposition.
- Looking Ahead to Calculus These margin notes offer glimpses of how the algebraic topics currently being studied are used in calculus.
- Connections This boxed feature provides connections to the real world or to other mathematical concepts, historical background, and thought-provoking questions for writing, class discussion, or group work.
- Relating Concepts Exercises Appearing in selected exercise sets, these sets of problems help students tie together topics and develop problem-solving skills as they compare and contrast ideas, identify and describe patterns, and extend concepts to new situations. These exercises make great collaborative activities for pairs or small groups of students.

**New To This Edition **

- Examples We have added even more examples in this edition. Step-by-step solutions to examples are now easily identified using a Solution head. We have carefully polished all solutions and incorporated more side comments and explanations, including helpful section references to previously-covered material. Selected examples continue to provide graphing calculator solutions alongside traditional algebraic solutions. The graphing calculator solutions can be easily omitted if desired.
- Now try Exercises To actively engage students in the learning process, each example now concludes with a reference to one or more parallel, odd-numbered exercises from the corresponding exercise set. In this way, students are able to immediately apply and reinforce the concepts and skills presented in the examples.
- Exercise Sets We have taken special care to respond to the suggestions of users and reviewers and have added many new exercises to this edition based on their feedback. As a result, the text includes more problems than ever to provide students with ample opportunities to practice, apply, connect, and extend concepts and skills. We have included writing exercises and optional graphing calculator problems as well as multiple-choice, matching, true/false, and completion problems. Concept Check problems, which focus on mathematical thinking and conceptual understanding, were well received in the previous edition and have been expanded in this edition.
- Solutions to Selected Exercises Exercise numbers enclosed in a blue circle indicate that a complete solution for the problem is included at the back of the text. These new solutions are given for selected exercises that extend the skills and concepts presented in the section examples. There are approximately 3 to 5 per section.
- Summary Exercises These new sets of in-chapter exercises in most chapters provide students with the all-important mixed review problems they need to synthesize concepts and select appropriate solution methods.
- Function Boxes Beginning in Chapter 2, functions are a unifying theme throughout the remainder of the text. To that end, special function boxes offer a comprehensive, visual introduction to each class of function and also serve as an excellent resource for student reference and review throughout the course. Each function box includes a table of values alongside traditional and calculator graphs, as well as the domain, range, and other specific information about the function.
- Chapter Reviews Each Chapter ends with an expanded Summary, featuring a section-by-section list of Key Terms, New Symbols, and a Quick Review of important Concepts, presented alongside corresponding all-new Examples. A comprehensive set of Review Excercises and a Chapter Test are also provided.
- Quantitative Reasoning Now appearing at the end of each chapter, these problems enable students to apply algebraic concepts to real-life situations, such as financial planning for retirement or determining the value of a college education. A photo highlights each problem.
- Glossary As an additional student study aid, a comprehensive glossary of key terms from throughout the text is provided at the back of the book.
- New Annotated Instructor's Edition --This special edition of the text provides answers to almost all text exercises in color on the page that the exercise appears. This provides the instructor with immediate access to answers without searching the back of the book.

Table of Contents

**R. Review of Basic Concepts. **

Real Numbers and Their Properties.

Order and Absolute Value.

Polynomials.

Factoring Polynomials.

Rational Expressions.

Rational Exponents.

Radical Expressions.

**1. Equations and Inequalities. **

Linear Equations.

Applications and Modeling with Linear Equations.

Complex Numbers.

Quadratic Equations.

Applications and Modeling with Quadratic Equations.

Other Types of Equations.

Inequalities.

Absolute Value Equations and Inequalities.

**2. Graphs and Functions. **

Graphs of Equations.

Functions.

Linear Functions.

Equations of Lines; Curve Fitting.

Graphs of Basic Functions.

Graphing Techniques.

Function Operations and Composition.

**3. Polynomial and Rational Functions. **

Quadratic Functions and Models.

Synthetic Division.

Zeros of Polynomial Functions.

Polynomial Functions: Graphs, Applications, and Models.

Rational Functions: Graphs, Applications, and Models.

Variation.

**4. Exponential and Logarithmic Functions. **

Inverse Functions.

Exponential Functions.

Logarithmic Functions.

Evaluating Logarithms and the Change-of-Base Theorem.

Exponential and Logarithmic Equations.

Applications and Models of Exponential Growth and Decay.

**5. Trigonometric Functions. **

Angles.

Trigonometric Functions.

Evaluating Trigonometric Functions.

Solving Right Triangles.

**6. The Circular Functions and Their Graphs. **

Radian Measure.

The Unit Circle and Circular Functions.

Graphs of the Sine and Cosine Functions.

Graphs of the Other Circular Functions.

Harmonic Motion.

**7. Trigonometric Identities and Equations. **

Fundamental Identities.

Verifying Trigonometric Identities.

Sum and Difference Identities.

Double-Angle Identities and Half-Angle Identities.

Inverse Circular Functions.

Trigonometric Equations.

Equations Involving Inverse Trigonometric Functions.

**8. Applications of Trigonometry. **

The Law of Sines.

The Law of Cosines.

Vectors, Operations, and the Dot Product.

Applications of Vectors.

Trigonometric (Polar) Form of Complex Numbers; Products and Quotients.

DeMoivre's Theorem; Powers and Roots of Complex Numbers.

Polar Equations and Graphs.

Parametric Equations, Graphs, and Applications.

**9. Systems and Matrices. **

Systems of Linear Equations.

Matrix Solution of Linear Systems.

Determinant Solution of Linear Systems.

Partial Fractions.

Nonlinear Systems of Equations.

Systems of Inequalities and Linear Programming.

Properties of Matrices.

Matrix Inverses.

**10. Analytic Geometry. **

Parabolas.

Ellipses.

Hyperbolas.

Summary of the Conic Sections.

**11. Further Topics in Algebra. **

Sequences and Series.

Arithmetic Sequences and Series.

Geometric Sequences and Series.

The Binomial Theorem.

Mathematical Induction.

Counting Theory.

Basics of Probability.

Appendix A. Polar Form of Conic Sections.

Appendix B. Rotation of Axes.

Glossary.

Solutions to Selected Exercises.

Answers to Selected Exercises.

Index of Applications.

Index.

Appendix C: Geometry Formulas.

Publisher Info

Publisher: Addison-Wesley Longman, Inc.

Published: 2005

International: No

Published: 2005

International: No

Focusing on helping students to develop both the conceptual understanding and the analytical skills necessary to experience success in mathematics, we present each mathematical topic in this text using a carefully developed learning system to actively engage students in the learning process. We have tried to address the diverse needs of today's students through a more open design, updated figures and graphs, helpful features, careful explanations of topics, and a comprehensive package of supplements and study aids. Students will benefit from the text's student-oriented approach. We believe instructors will particularly welcome the new Annotated Instructor's Edition, which provides answers in the margin to almost all exercises, plus helpful Teaching Tips.

**Features **

- Real-Life Applications We are always on the lookout for interesting data to use in real-life applications. As a result, we have updated or incorporated many new or examples and exercises from fields such as business, pop culture, sports, life sciences, and environmental studies that show the relevance of algebra to daily life. Applications that feature mathematical modeling are labeled with a Modeling head. All applications are titled, and a comprehensive Index of Applications is included at the back of the text.
- Use of Technology As in the previous edition, we have integrated the use of graphing calculators where appropriate, although graphing technology is not a central feature of this text. We continue to stress that graphing calculators are an aid to understanding and that students must master the underlying mathematical concepts first. We have included graphing calculator solutions for selected examples and continue to mark all graphing calculator notes and exercises that use graphing calculators with an icon for easy identification and added flexibility. This graphing calculator material is optional and can be omitted without loss of continuity.
- Cautions and Notes We often give students warnings of common errors and emphasize important ideas in Caution and Note comments that appear throughout the exposition.
- Looking Ahead to Calculus These margin notes offer glimpses of how the algebraic topics currently being studied are used in calculus.
- Connections This boxed feature provides connections to the real world or to other mathematical concepts, historical background, and thought-provoking questions for writing, class discussion, or group work.
- Relating Concepts Exercises Appearing in selected exercise sets, these sets of problems help students tie together topics and develop problem-solving skills as they compare and contrast ideas, identify and describe patterns, and extend concepts to new situations. These exercises make great collaborative activities for pairs or small groups of students.

**New To This Edition **

- Examples We have added even more examples in this edition. Step-by-step solutions to examples are now easily identified using a Solution head. We have carefully polished all solutions and incorporated more side comments and explanations, including helpful section references to previously-covered material. Selected examples continue to provide graphing calculator solutions alongside traditional algebraic solutions. The graphing calculator solutions can be easily omitted if desired.
- Now try Exercises To actively engage students in the learning process, each example now concludes with a reference to one or more parallel, odd-numbered exercises from the corresponding exercise set. In this way, students are able to immediately apply and reinforce the concepts and skills presented in the examples.
- Exercise Sets We have taken special care to respond to the suggestions of users and reviewers and have added many new exercises to this edition based on their feedback. As a result, the text includes more problems than ever to provide students with ample opportunities to practice, apply, connect, and extend concepts and skills. We have included writing exercises and optional graphing calculator problems as well as multiple-choice, matching, true/false, and completion problems. Concept Check problems, which focus on mathematical thinking and conceptual understanding, were well received in the previous edition and have been expanded in this edition.
- Solutions to Selected Exercises Exercise numbers enclosed in a blue circle indicate that a complete solution for the problem is included at the back of the text. These new solutions are given for selected exercises that extend the skills and concepts presented in the section examples. There are approximately 3 to 5 per section.
- Summary Exercises These new sets of in-chapter exercises in most chapters provide students with the all-important mixed review problems they need to synthesize concepts and select appropriate solution methods.
- Function Boxes Beginning in Chapter 2, functions are a unifying theme throughout the remainder of the text. To that end, special function boxes offer a comprehensive, visual introduction to each class of function and also serve as an excellent resource for student reference and review throughout the course. Each function box includes a table of values alongside traditional and calculator graphs, as well as the domain, range, and other specific information about the function.
- Chapter Reviews Each Chapter ends with an expanded Summary, featuring a section-by-section list of Key Terms, New Symbols, and a Quick Review of important Concepts, presented alongside corresponding all-new Examples. A comprehensive set of Review Excercises and a Chapter Test are also provided.
- Quantitative Reasoning Now appearing at the end of each chapter, these problems enable students to apply algebraic concepts to real-life situations, such as financial planning for retirement or determining the value of a college education. A photo highlights each problem.
- Glossary As an additional student study aid, a comprehensive glossary of key terms from throughout the text is provided at the back of the book.
- New Annotated Instructor's Edition --This special edition of the text provides answers to almost all text exercises in color on the page that the exercise appears. This provides the instructor with immediate access to answers without searching the back of the book.

**R. Review of Basic Concepts. **

Real Numbers and Their Properties.

Order and Absolute Value.

Polynomials.

Factoring Polynomials.

Rational Expressions.

Rational Exponents.

Radical Expressions.

**1. Equations and Inequalities. **

Linear Equations.

Applications and Modeling with Linear Equations.

Complex Numbers.

Quadratic Equations.

Applications and Modeling with Quadratic Equations.

Other Types of Equations.

Inequalities.

Absolute Value Equations and Inequalities.

**2. Graphs and Functions. **

Graphs of Equations.

Functions.

Linear Functions.

Equations of Lines; Curve Fitting.

Graphs of Basic Functions.

Graphing Techniques.

Function Operations and Composition.

**3. Polynomial and Rational Functions. **

Quadratic Functions and Models.

Synthetic Division.

Zeros of Polynomial Functions.

Polynomial Functions: Graphs, Applications, and Models.

Rational Functions: Graphs, Applications, and Models.

Variation.

**4. Exponential and Logarithmic Functions. **

Inverse Functions.

Exponential Functions.

Logarithmic Functions.

Evaluating Logarithms and the Change-of-Base Theorem.

Exponential and Logarithmic Equations.

Applications and Models of Exponential Growth and Decay.

**5. Trigonometric Functions. **

Angles.

Trigonometric Functions.

Evaluating Trigonometric Functions.

Solving Right Triangles.

**6. The Circular Functions and Their Graphs. **

Radian Measure.

The Unit Circle and Circular Functions.

Graphs of the Sine and Cosine Functions.

Graphs of the Other Circular Functions.

Harmonic Motion.

**7. Trigonometric Identities and Equations. **

Fundamental Identities.

Verifying Trigonometric Identities.

Sum and Difference Identities.

Double-Angle Identities and Half-Angle Identities.

Inverse Circular Functions.

Trigonometric Equations.

Equations Involving Inverse Trigonometric Functions.

**8. Applications of Trigonometry. **

The Law of Sines.

The Law of Cosines.

Vectors, Operations, and the Dot Product.

Applications of Vectors.

Trigonometric (Polar) Form of Complex Numbers; Products and Quotients.

DeMoivre's Theorem; Powers and Roots of Complex Numbers.

Polar Equations and Graphs.

Parametric Equations, Graphs, and Applications.

**9. Systems and Matrices. **

Systems of Linear Equations.

Matrix Solution of Linear Systems.

Determinant Solution of Linear Systems.

Partial Fractions.

Nonlinear Systems of Equations.

Systems of Inequalities and Linear Programming.

Properties of Matrices.

Matrix Inverses.

**10. Analytic Geometry. **

Parabolas.

Ellipses.

Hyperbolas.

Summary of the Conic Sections.

**11. Further Topics in Algebra. **

Sequences and Series.

Arithmetic Sequences and Series.

Geometric Sequences and Series.

The Binomial Theorem.

Mathematical Induction.

Counting Theory.

Basics of Probability.

Appendix A. Polar Form of Conic Sections.

Appendix B. Rotation of Axes.

Glossary.

Solutions to Selected Exercises.

Answers to Selected Exercises.

Index of Applications.

Index.

Appendix C: Geometry Formulas.