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by Raymond A. Barnett, Michael R. Ziegler and Karl E. Byleen

Edition: 6TH 08Copyright: 2008

Publisher: McGraw-Hill Publishing Company

Published: 2008

International: No

Raymond A. Barnett, Michael R. Ziegler and Karl E. Byleen

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The Barnett, Ziegler, Byleen College Algebra series is designed to be user friendly and to maximize student comprehension, emphasizing computational skills, ideas, and problem solving as opposed to mathematical theory. Suitable for a one or two semester college algebra with trigonometry or precalculus course, Precalculus with Limits introduces a unit circle approach to trigonometry and includes a chapter on limits to provide students with a solid foundation for calculus concepts.

The large number of pedagogical devices employed in this text will guide a student through the course. Integrated throughout the text, students and instructors will find Explore-Discuss boxes which encourage students to think critically about mathematical concepts. In each section, the worked examples are followed by matched problems that reinforce the concept being taught. In addition, the text contains an abundance of exercises and applications that will convince students that math is useful. A MathZone site featuring algorithmic exercises, videos, and other resources accompanies the text.

**Chapter R: Basic Algebraic Operations**

R-1 Algebra and Real Numbers

R-2 Exponents

R-3 Radicals

R-4 Polynomials: Basic Operations

R-5 Polynomials: Factoring

R-6 Rational Expressions: Basic Operations

Chapter R Review

Chapter R Review Exercises

Chapter R Group Activity: Rational and Irrational Numbers

**Chapter 1: Equations and Inequalities**

1-1 Linear Equations and Applications

1-2 Linear Inequalities

1-3 Absolute Value in Equations and Inequalities

1-4 Complex Numbers

1-5 Quadratic Equations and Applications

1-6 Additional Equation-Solving Techniques

Chapter 1 Review

Chapter 1 Review Exercises

Chapter 1 Group Activity: Solving a Cubic Equation

**Chapter 2: Graphs**

2-1 Cartesian Coordinate System

2-2 Distance in the Plane

2-3 Equations of a Line

2-4 Linear Equations and Models

Chapter 2 Review

Chapter 2 Review Exercises

Chapter 2 Group Activity: Rates of Change

**Chapter 3: Functions**

3-1 Functions

3-2 Graphing Functions

3-3 Transformations of Functions

3-4 Quadratic Functions

3-5 Operations on Functions; Composition

3-6 Inverse Functions

Chapter 3 Review

Chapter 3 Review Exercises

Chapter 3 Group Activity: Mathematical Modeling: Choosing a Long-Distance Calling Plan

Cumulative Review Exercises Chapters 1-3

**Chapter 4: Polynomials and Rational Functions**

4-1 Polynomial Functions and Models

4-2 Real Zeros and Polynomial Inequalities

4-3 Complex Zeros and Rational Zeros of Polynomials

4-4 Rational Functions and Inequalities

4-5 Variation and Modeling

Chapter 4 Review

Chapter 4 Review Exercises

Chapter 4 Group Activity: Interpolating Polynomials

**Chapter 5: Exponential and Logarithmic Functions**

5-1 Exponential Functions

5-2 Exponential Models

5-3 Logarithmic Functions

5-4 Logarithmic Models

5-5 Exponential and Logarithmic Equations

Chapter 5 Review

Chapter 5 Review Exercises

Chapter 5 Group Activity: Comparing Regression Models

Cumulative Review Exercises Chapters 4-5

**Chapter 6: Trigonometric Functions**

6-1 Angles and Their Measure

6-2 Trigonometric Functions: A Unit Circle Approach

6-3 Solving Right Triangles

6-4 Properties of Trigonometric Functions

6-5 More General Trigonometric Functions and Models

6-6 Inverse Trigonometric Functions

Chapter 6 Review

Chapter 6 Review Exercises

Chapter 6 Group Activity: A Predator-Prey Analysis Involving Mountain Lions and Deer

**Chapter 7: Trigonometric Identities and Conditional Equations**

7-1 Basic Identities and Their Use

7-2 Sum, Difference, and Cofunction Identities

7-3 Double-Angle and Half-Angle Identities

7-4 Product-Sum and Sum-Product Identities

7-5 Trigonometric Equations

Chapter 7 Review

Chapter 7 Review Exercises

Chapter 7 Group Activity: From M sin Bt + N cos Bt to A sin (Bt + C): A Harmonic Analysis Tool

**Chapter 8: Additional Topics in Trigonometry**

8-1 Law of Sines

8-2 Law of Cosines

8-3 Vectors in the Plane

8-4 Polar Coordinates and Graphs

8-5 Complex Numbers and De Moivre's Theorem

Chapter 8 Review

Chapter 8 Review Exercises

Chapter 8 Group Activity: Conic Sections and Planetary Orbits

Cumulative Review Exercises Chapters 6-8

**Chapter 9: Additional Topics in Analytic Geometry**

9-1 Conic Sections; Parabolas

9-2 Ellipse

9-3 Hyperbola

9-4 Translation and Rotation of Axes

Chapter 9 Review

Chapter 9 Review Exercises

Chapter 9 Group Activity: Focal Chords

**Chapter 10: Systems of Equations and Inequalities; Matrices**

10-1 Systems of Linear Equations in Two Variables

10-2 Systems of Linear Equations in Three Variables

10-3 Systems of Linear Equations: Gauss-Jordan Elimination

10-4 Matrix Operations

10-5 Systems of Linear Equations: Matrix Inverse Methods

10-6 Systems of Nonlinear Equations

10-7 Systems of Linear Inequalities in Two Variables

10-8 Linear Programming

Chapter 10 Review

Chapter 10 Review Exercises

Chapter 10 Group Activity: Modeling With Systems of Linear Equations

**Chapter 11: Sequences, Induction, and Probability**

11-1 Sequences and Series

11-2 Mathematical Induction

11-3 Arithmetic and Geometric Sequences

11-4 Multiplication Principle, Permutations, and Combinations

11-5 Sample Spaces and Probability

11-6 Binomial Formula

Chapter 11 Review

Chapter 11 Review Exercises

Chapter 11 Group Activity: Sequences Specified by Recursion Formulas

Cumulative Review Exercises Chapters 9-11

**Chapter 12 Limits: An Introduction to Calculus**

12-1 Introduction to Limits

12-2 Computing Limits Algebraically

12-3 Limits at Infinity

12-4 The Derivative

12-5 Area and Calculus

Chapter 12 Review

Chapter 12 Review Exercises

Chapter 12 Group Activity: Derivatives of Exponential and Log Functions

Appendix A: Special Topics

A-1 Scientific Notation and Significant Digits

A-2 Partial Fractions

A-3 Parametric Equations

Appendix B: Geometric Formulas

Student Answers

Subject Index

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Summary

The Barnett, Ziegler, Byleen College Algebra series is designed to be user friendly and to maximize student comprehension, emphasizing computational skills, ideas, and problem solving as opposed to mathematical theory. Suitable for a one or two semester college algebra with trigonometry or precalculus course, Precalculus with Limits introduces a unit circle approach to trigonometry and includes a chapter on limits to provide students with a solid foundation for calculus concepts.

The large number of pedagogical devices employed in this text will guide a student through the course. Integrated throughout the text, students and instructors will find Explore-Discuss boxes which encourage students to think critically about mathematical concepts. In each section, the worked examples are followed by matched problems that reinforce the concept being taught. In addition, the text contains an abundance of exercises and applications that will convince students that math is useful. A MathZone site featuring algorithmic exercises, videos, and other resources accompanies the text.

Table of Contents

**Chapter R: Basic Algebraic Operations**

R-1 Algebra and Real Numbers

R-2 Exponents

R-3 Radicals

R-4 Polynomials: Basic Operations

R-5 Polynomials: Factoring

R-6 Rational Expressions: Basic Operations

Chapter R Review

Chapter R Review Exercises

Chapter R Group Activity: Rational and Irrational Numbers

**Chapter 1: Equations and Inequalities**

1-1 Linear Equations and Applications

1-2 Linear Inequalities

1-3 Absolute Value in Equations and Inequalities

1-4 Complex Numbers

1-5 Quadratic Equations and Applications

1-6 Additional Equation-Solving Techniques

Chapter 1 Review

Chapter 1 Review Exercises

Chapter 1 Group Activity: Solving a Cubic Equation

**Chapter 2: Graphs**

2-1 Cartesian Coordinate System

2-2 Distance in the Plane

2-3 Equations of a Line

2-4 Linear Equations and Models

Chapter 2 Review

Chapter 2 Review Exercises

Chapter 2 Group Activity: Rates of Change

**Chapter 3: Functions**

3-1 Functions

3-2 Graphing Functions

3-3 Transformations of Functions

3-4 Quadratic Functions

3-5 Operations on Functions; Composition

3-6 Inverse Functions

Chapter 3 Review

Chapter 3 Review Exercises

Chapter 3 Group Activity: Mathematical Modeling: Choosing a Long-Distance Calling Plan

Cumulative Review Exercises Chapters 1-3

**Chapter 4: Polynomials and Rational Functions**

4-1 Polynomial Functions and Models

4-2 Real Zeros and Polynomial Inequalities

4-3 Complex Zeros and Rational Zeros of Polynomials

4-4 Rational Functions and Inequalities

4-5 Variation and Modeling

Chapter 4 Review

Chapter 4 Review Exercises

Chapter 4 Group Activity: Interpolating Polynomials

**Chapter 5: Exponential and Logarithmic Functions**

5-1 Exponential Functions

5-2 Exponential Models

5-3 Logarithmic Functions

5-4 Logarithmic Models

5-5 Exponential and Logarithmic Equations

Chapter 5 Review

Chapter 5 Review Exercises

Chapter 5 Group Activity: Comparing Regression Models

Cumulative Review Exercises Chapters 4-5

**Chapter 6: Trigonometric Functions**

6-1 Angles and Their Measure

6-2 Trigonometric Functions: A Unit Circle Approach

6-3 Solving Right Triangles

6-4 Properties of Trigonometric Functions

6-5 More General Trigonometric Functions and Models

6-6 Inverse Trigonometric Functions

Chapter 6 Review

Chapter 6 Review Exercises

Chapter 6 Group Activity: A Predator-Prey Analysis Involving Mountain Lions and Deer

**Chapter 7: Trigonometric Identities and Conditional Equations**

7-1 Basic Identities and Their Use

7-2 Sum, Difference, and Cofunction Identities

7-3 Double-Angle and Half-Angle Identities

7-4 Product-Sum and Sum-Product Identities

7-5 Trigonometric Equations

Chapter 7 Review

Chapter 7 Review Exercises

Chapter 7 Group Activity: From M sin Bt + N cos Bt to A sin (Bt + C): A Harmonic Analysis Tool

**Chapter 8: Additional Topics in Trigonometry**

8-1 Law of Sines

8-2 Law of Cosines

8-3 Vectors in the Plane

8-4 Polar Coordinates and Graphs

8-5 Complex Numbers and De Moivre's Theorem

Chapter 8 Review

Chapter 8 Review Exercises

Chapter 8 Group Activity: Conic Sections and Planetary Orbits

Cumulative Review Exercises Chapters 6-8

**Chapter 9: Additional Topics in Analytic Geometry**

9-1 Conic Sections; Parabolas

9-2 Ellipse

9-3 Hyperbola

9-4 Translation and Rotation of Axes

Chapter 9 Review

Chapter 9 Review Exercises

Chapter 9 Group Activity: Focal Chords

**Chapter 10: Systems of Equations and Inequalities; Matrices**

10-1 Systems of Linear Equations in Two Variables

10-2 Systems of Linear Equations in Three Variables

10-3 Systems of Linear Equations: Gauss-Jordan Elimination

10-4 Matrix Operations

10-5 Systems of Linear Equations: Matrix Inverse Methods

10-6 Systems of Nonlinear Equations

10-7 Systems of Linear Inequalities in Two Variables

10-8 Linear Programming

Chapter 10 Review

Chapter 10 Review Exercises

Chapter 10 Group Activity: Modeling With Systems of Linear Equations

**Chapter 11: Sequences, Induction, and Probability**

11-1 Sequences and Series

11-2 Mathematical Induction

11-3 Arithmetic and Geometric Sequences

11-4 Multiplication Principle, Permutations, and Combinations

11-5 Sample Spaces and Probability

11-6 Binomial Formula

Chapter 11 Review

Chapter 11 Review Exercises

Chapter 11 Group Activity: Sequences Specified by Recursion Formulas

Cumulative Review Exercises Chapters 9-11

**Chapter 12 Limits: An Introduction to Calculus**

12-1 Introduction to Limits

12-2 Computing Limits Algebraically

12-3 Limits at Infinity

12-4 The Derivative

12-5 Area and Calculus

Chapter 12 Review

Chapter 12 Review Exercises

Chapter 12 Group Activity: Derivatives of Exponential and Log Functions

Appendix A: Special Topics

A-1 Scientific Notation and Significant Digits

A-2 Partial Fractions

A-3 Parametric Equations

Appendix B: Geometric Formulas

Student Answers

Subject Index

Publisher Info

Publisher: McGraw-Hill Publishing Company

Published: 2008

International: No

Published: 2008

International: No

The large number of pedagogical devices employed in this text will guide a student through the course. Integrated throughout the text, students and instructors will find Explore-Discuss boxes which encourage students to think critically about mathematical concepts. In each section, the worked examples are followed by matched problems that reinforce the concept being taught. In addition, the text contains an abundance of exercises and applications that will convince students that math is useful. A MathZone site featuring algorithmic exercises, videos, and other resources accompanies the text.

**Chapter R: Basic Algebraic Operations**

R-1 Algebra and Real Numbers

R-2 Exponents

R-3 Radicals

R-4 Polynomials: Basic Operations

R-5 Polynomials: Factoring

R-6 Rational Expressions: Basic Operations

Chapter R Review

Chapter R Review Exercises

Chapter R Group Activity: Rational and Irrational Numbers

**Chapter 1: Equations and Inequalities**

1-1 Linear Equations and Applications

1-2 Linear Inequalities

1-3 Absolute Value in Equations and Inequalities

1-4 Complex Numbers

1-5 Quadratic Equations and Applications

1-6 Additional Equation-Solving Techniques

Chapter 1 Review

Chapter 1 Review Exercises

Chapter 1 Group Activity: Solving a Cubic Equation

**Chapter 2: Graphs**

2-1 Cartesian Coordinate System

2-2 Distance in the Plane

2-3 Equations of a Line

2-4 Linear Equations and Models

Chapter 2 Review

Chapter 2 Review Exercises

Chapter 2 Group Activity: Rates of Change

**Chapter 3: Functions**

3-1 Functions

3-2 Graphing Functions

3-3 Transformations of Functions

3-4 Quadratic Functions

3-5 Operations on Functions; Composition

3-6 Inverse Functions

Chapter 3 Review

Chapter 3 Review Exercises

Chapter 3 Group Activity: Mathematical Modeling: Choosing a Long-Distance Calling Plan

Cumulative Review Exercises Chapters 1-3

**Chapter 4: Polynomials and Rational Functions**

4-1 Polynomial Functions and Models

4-2 Real Zeros and Polynomial Inequalities

4-3 Complex Zeros and Rational Zeros of Polynomials

4-4 Rational Functions and Inequalities

4-5 Variation and Modeling

Chapter 4 Review

Chapter 4 Review Exercises

Chapter 4 Group Activity: Interpolating Polynomials

**Chapter 5: Exponential and Logarithmic Functions**

5-1 Exponential Functions

5-2 Exponential Models

5-3 Logarithmic Functions

5-4 Logarithmic Models

5-5 Exponential and Logarithmic Equations

Chapter 5 Review

Chapter 5 Review Exercises

Chapter 5 Group Activity: Comparing Regression Models

Cumulative Review Exercises Chapters 4-5

**Chapter 6: Trigonometric Functions**

6-1 Angles and Their Measure

6-2 Trigonometric Functions: A Unit Circle Approach

6-3 Solving Right Triangles

6-4 Properties of Trigonometric Functions

6-5 More General Trigonometric Functions and Models

6-6 Inverse Trigonometric Functions

Chapter 6 Review

Chapter 6 Review Exercises

Chapter 6 Group Activity: A Predator-Prey Analysis Involving Mountain Lions and Deer

**Chapter 7: Trigonometric Identities and Conditional Equations**

7-1 Basic Identities and Their Use

7-2 Sum, Difference, and Cofunction Identities

7-3 Double-Angle and Half-Angle Identities

7-4 Product-Sum and Sum-Product Identities

7-5 Trigonometric Equations

Chapter 7 Review

Chapter 7 Review Exercises

Chapter 7 Group Activity: From M sin Bt + N cos Bt to A sin (Bt + C): A Harmonic Analysis Tool

**Chapter 8: Additional Topics in Trigonometry**

8-1 Law of Sines

8-2 Law of Cosines

8-3 Vectors in the Plane

8-4 Polar Coordinates and Graphs

8-5 Complex Numbers and De Moivre's Theorem

Chapter 8 Review

Chapter 8 Review Exercises

Chapter 8 Group Activity: Conic Sections and Planetary Orbits

Cumulative Review Exercises Chapters 6-8

**Chapter 9: Additional Topics in Analytic Geometry**

9-1 Conic Sections; Parabolas

9-2 Ellipse

9-3 Hyperbola

9-4 Translation and Rotation of Axes

Chapter 9 Review

Chapter 9 Review Exercises

Chapter 9 Group Activity: Focal Chords

**Chapter 10: Systems of Equations and Inequalities; Matrices**

10-1 Systems of Linear Equations in Two Variables

10-2 Systems of Linear Equations in Three Variables

10-3 Systems of Linear Equations: Gauss-Jordan Elimination

10-4 Matrix Operations

10-5 Systems of Linear Equations: Matrix Inverse Methods

10-6 Systems of Nonlinear Equations

10-7 Systems of Linear Inequalities in Two Variables

10-8 Linear Programming

Chapter 10 Review

Chapter 10 Review Exercises

Chapter 10 Group Activity: Modeling With Systems of Linear Equations

**Chapter 11: Sequences, Induction, and Probability**

11-1 Sequences and Series

11-2 Mathematical Induction

11-3 Arithmetic and Geometric Sequences

11-4 Multiplication Principle, Permutations, and Combinations

11-5 Sample Spaces and Probability

11-6 Binomial Formula

Chapter 11 Review

Chapter 11 Review Exercises

Chapter 11 Group Activity: Sequences Specified by Recursion Formulas

Cumulative Review Exercises Chapters 9-11

**Chapter 12 Limits: An Introduction to Calculus**

12-1 Introduction to Limits

12-2 Computing Limits Algebraically

12-3 Limits at Infinity

12-4 The Derivative

12-5 Area and Calculus

Chapter 12 Review

Chapter 12 Review Exercises

Chapter 12 Group Activity: Derivatives of Exponential and Log Functions

Appendix A: Special Topics

A-1 Scientific Notation and Significant Digits

A-2 Partial Fractions

A-3 Parametric Equations

Appendix B: Geometric Formulas

Student Answers

Subject Index