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by Ron Larson, Robert P. Hostetler and Bruce H. Edwards

Edition: 5TH 08Copyright: 2008

Publisher: Houghton Mifflin Harcourt

Published: 2008

International: No

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Part of the market-leading Graphing Approach Series by Larson, Hostetler, and Edwards, Precalculus Functions and Graphs: A Graphing Approach, 5/e, is an ideal student and instructor resource for courses that require the use of a graphing calculator. The quality and quantity of the exercises, combined with interesting applications and innovative resources, make teaching easier and help students succeed.

Continuing the series' emphasis on student support, the Fifth Edition introduces Prerequisite Skills Review. For selected examples throughout the text, the Prerequisite Skills Review directs students to previous sections in the text to review concepts and skills needed to master the material at hand. In addition, prerequisite skills review exercises in Eduspace (see below for description) are referenced in every exercise set.

The Larson team achieves accessibility through careful writing and design, including examples with detailed solutions that begin and end on the same page, which maximizes the readability of the text. Similarly, side-by-side solutions show algebraic, graphical, and numerical representations of the mathematics and support a variety of learning styles.

- New! The Nutshell Appendix reviews the essentials of each function, discussed in the Library of Functions feature, and offers study capsules with properties, methods, and examples of the major concepts covered in the textbook. This appendix is an ideal study aid for students.
- New! Progressive Summaries outline newly introduced topics every three chapters and contextualize them within the framework of the course.
- New! Make a Decision exercises--extended modeling applications presented at the end of selected exercise sets--give students the opportunity to apply the mathematical concepts and techniques they've learned to large sets of real data.
- Updated! The Library of Functions, threaded throughout the text, defines each elementary function and its characteristics at first point of use. The Fifth Edition incorporates new exercises that tests students' understanding of these functions. All elementary functions are also presented in a summary on the front endpapers of the text for convenient reference.
- Updated! The Chapter Summaries have been updated to include the Key Terms and Key concepts that are covered in the chapter. These chapter summaries are an effective study aid because they provide a single point of reference for review.
- Updated! The Proofs of Selected Theorems are now presented at the end of each chapter for easy reference.
- The Larson team provides an abundance of features that help students use technology to visualize and understand mathematical concepts. Technology Tips point out the pros and cons of technology use in certain mathematical situations. They also provide alternative methods of solving or checking a problem using a graphing calculator. Students may sometimes be misled by the visuals generated by graphing calculators, so the authors use color to enhance the graphing calculator displays in the textbook, where appropriate. This enables students to visualize concepts accurately and efficiently. Technology Support notes appear throughout the text and refer students to the Technology Support Appendix, where they can learn how to use specific graphing calculator features to enhance their understanding of the concepts presented. The Technology Support notes also direct students to the Graphing Technology Guide, on the textbook's website, for keystroke support for numerous calculator models.
- Carefully positioned throughout the text, Explorations engage students in active discovery of mathematical concepts, strengthening critical thinking skills and helping them to develop an intuitive understanding of theoretical concepts.
- What You Should Learn and Why You Should Learn It appears at the beginning of each chapter and section, offering students a succinct list of the concepts they will soon encounter. Additionally, this feature refers students to an application in the exercise set which helps put the math concept into a real-life context so students can understand it better.
- To help prepare students who intend to move on to Calculus, the authors have placed an icon next to algebraic techniques that are used in Calculus.

**1. Functions and Their Graphs Introduction to Library of Functions**

1.1 Lines in the Plane

1.2 Functions

1.3 Graphs of Functions

1.4 Shifting, Reflection, and Stretching Graphs

1.5 Combinations of Functions

1.6 Inverse Functions

1.7 Linear Models and Scatter Plots

**2. Polynomial and Rational Functions**

2.1 Quadratic Functions

2.2 Polynomial Functions of Higher Degree

2.3 Real Zeros of Polynomial Functions

2.4 Complex Numbers

2.5 The Fundamental Theorem of Algebra

2.6 Rational Functions and Asymptotes

2.7 Graphs of Rational Functions

2.8 Quadratic Models

**Progressive Summary: Chapters 1-2 3. Exponential and Logarithmic Functions**

3.1 Exponential Functions and Their Graphs

3.2 Logarithmic Functions and Their Graphs

3.3 Properties of Logarithms

3.4 Solving Exponential and Logarithmic Equations

3.5 Exponential and Logarithmic Models

3.6 Nonlinear Models

**Cumulative Review: Chapters 1-3 Progressive Summary: Chapters 1-3 4. Trigonometric Functions**

4.1 Radian and Degree Measure

4.2 Trigonometric Functions: The Unit Circle

4.3 Right Triangle Trigonometry

4.4 Trigonometric Functions of Any Angle

4.5 Graphs of Sine and Cosine Functions

4.6 Graphs of Other Trigonometric Functions

4.7 Inverse Trigonometric Functions

4.8 Applications and Models

**5. Analytic Trigonometry**

5.1 Using Fundamental Identities

5.2 Verifying Trigonometric Identities

5.3 Solving Trigonometric Equations

5.4 Sum and Difference Formulas

5.5 Multiple-Angle and Product-to-Sum Formulas

**6. Additional Topics in Trigonometry**

6.1 Law of Sines

6.2 Law of Cosines

6.3 Vectors in the Plane

6.4 Vectors and Dot Products

6.5 Trigonometric Form of a Complex Number

**Cumulative Test: Chapters 4-6 Progressive Summary: Chapters 1-6 7. Linear Systems and Matrices**

7.1 Solving Systems of Equations

7.2 Systems of Linear Equations in Two Variables

7.3 Multivariable Linear Systems

7.4 Matrices and Systems of Equations

7.5 Operations with Matrices

7.6 The Inverse of a Square Matrix

7.7 The Determinant of a Square Matrix

7.8 Applications of Matrices and Determinants

**8. Sequences, Series, and Probability**

8.1 Sequence and Series

8.2 Arithmetic Sequences and Partial Sums

8.3 Geometric Sequences and Series

8.4 Mathematical Induction

8.5 The Binomial Theorem

8.6 Counting Principals

8.7 Probability

**Progressive Summary: Chapters 1-8 9. Topics in Analytic Geometry**

9.1 Conics: Circles and Parabolas

9.2 Conics: Ellipses

9.3 Conics: Hyperbolas

9.4 Rotation and Systems of Quadratic Equations

9.5 Parametric Equations

9.6 Polar Coordinates

9.7 Graphs of Polar Equations

9.8 Polar Equations of Conics

**Cumulative Test: Chapters 7-9 10. Analytic Geometry in Three Dimensions**

10.1 The Three-Dimensional Coordinate System

10.2 Vectors in Space

10.3 The Cross Product of Two Vectors

10.4 Lines and Planes in Space

**11. Limits and an Introduction to Calculus**

11.1 Introduction to Limits

11.2 Techniques for Evaluating Limits

11.3 The Tangent Line Problem

11.4 Limits at Infinity and Limits of Sequences

11.5 The Area Problem

**Cumulative Test: Chapters 10-11 Progressive Summary: Chapters 1-11 Appendix A. Technology Support Guide Appendix B. Review of Graphs, Equations, and Inequalities**

B.1 The Cartesian Plane

B.2 Graphs of Equations

B.3 Solving Quadratic Equations Algebraically and Graphically

B.4 Solving Other Equations Algebraically and Graphically

B.5 Solving Inequalities Algebraically and Graphically

B.6 Representing Data Graphically

**Appendix C. Concepts in Statistics**

C.1 Measures of Central Tendency and Dispersion

C.2 Least Squares Regression

**Appendix D. Variation**

D.1 Direct Variation

D.2 Direct Variation as an nth Power

D.3 Inverse Variation

D4 Joint Variation

**Appendix E. Solving Linear Equations and Inequalities Appendix F. Systems of Inequalities**

F.1 Solving Systems of Inequalities

F.2 Linear Programming

Appendix G Study Capsules

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Summary

Part of the market-leading Graphing Approach Series by Larson, Hostetler, and Edwards, Precalculus Functions and Graphs: A Graphing Approach, 5/e, is an ideal student and instructor resource for courses that require the use of a graphing calculator. The quality and quantity of the exercises, combined with interesting applications and innovative resources, make teaching easier and help students succeed.

Continuing the series' emphasis on student support, the Fifth Edition introduces Prerequisite Skills Review. For selected examples throughout the text, the Prerequisite Skills Review directs students to previous sections in the text to review concepts and skills needed to master the material at hand. In addition, prerequisite skills review exercises in Eduspace (see below for description) are referenced in every exercise set.

The Larson team achieves accessibility through careful writing and design, including examples with detailed solutions that begin and end on the same page, which maximizes the readability of the text. Similarly, side-by-side solutions show algebraic, graphical, and numerical representations of the mathematics and support a variety of learning styles.

- New! The Nutshell Appendix reviews the essentials of each function, discussed in the Library of Functions feature, and offers study capsules with properties, methods, and examples of the major concepts covered in the textbook. This appendix is an ideal study aid for students.
- New! Progressive Summaries outline newly introduced topics every three chapters and contextualize them within the framework of the course.
- New! Make a Decision exercises--extended modeling applications presented at the end of selected exercise sets--give students the opportunity to apply the mathematical concepts and techniques they've learned to large sets of real data.
- Updated! The Library of Functions, threaded throughout the text, defines each elementary function and its characteristics at first point of use. The Fifth Edition incorporates new exercises that tests students' understanding of these functions. All elementary functions are also presented in a summary on the front endpapers of the text for convenient reference.
- Updated! The Chapter Summaries have been updated to include the Key Terms and Key concepts that are covered in the chapter. These chapter summaries are an effective study aid because they provide a single point of reference for review.
- Updated! The Proofs of Selected Theorems are now presented at the end of each chapter for easy reference.
- The Larson team provides an abundance of features that help students use technology to visualize and understand mathematical concepts. Technology Tips point out the pros and cons of technology use in certain mathematical situations. They also provide alternative methods of solving or checking a problem using a graphing calculator. Students may sometimes be misled by the visuals generated by graphing calculators, so the authors use color to enhance the graphing calculator displays in the textbook, where appropriate. This enables students to visualize concepts accurately and efficiently. Technology Support notes appear throughout the text and refer students to the Technology Support Appendix, where they can learn how to use specific graphing calculator features to enhance their understanding of the concepts presented. The Technology Support notes also direct students to the Graphing Technology Guide, on the textbook's website, for keystroke support for numerous calculator models.
- Carefully positioned throughout the text, Explorations engage students in active discovery of mathematical concepts, strengthening critical thinking skills and helping them to develop an intuitive understanding of theoretical concepts.
- What You Should Learn and Why You Should Learn It appears at the beginning of each chapter and section, offering students a succinct list of the concepts they will soon encounter. Additionally, this feature refers students to an application in the exercise set which helps put the math concept into a real-life context so students can understand it better.
- To help prepare students who intend to move on to Calculus, the authors have placed an icon next to algebraic techniques that are used in Calculus.

Table of Contents

**1. Functions and Their Graphs Introduction to Library of Functions**

1.1 Lines in the Plane

1.2 Functions

1.3 Graphs of Functions

1.4 Shifting, Reflection, and Stretching Graphs

1.5 Combinations of Functions

1.6 Inverse Functions

1.7 Linear Models and Scatter Plots

**2. Polynomial and Rational Functions**

2.1 Quadratic Functions

2.2 Polynomial Functions of Higher Degree

2.3 Real Zeros of Polynomial Functions

2.4 Complex Numbers

2.5 The Fundamental Theorem of Algebra

2.6 Rational Functions and Asymptotes

2.7 Graphs of Rational Functions

2.8 Quadratic Models

**Progressive Summary: Chapters 1-2 3. Exponential and Logarithmic Functions**

3.1 Exponential Functions and Their Graphs

3.2 Logarithmic Functions and Their Graphs

3.3 Properties of Logarithms

3.4 Solving Exponential and Logarithmic Equations

3.5 Exponential and Logarithmic Models

3.6 Nonlinear Models

**Cumulative Review: Chapters 1-3 Progressive Summary: Chapters 1-3 4. Trigonometric Functions**

4.1 Radian and Degree Measure

4.2 Trigonometric Functions: The Unit Circle

4.3 Right Triangle Trigonometry

4.4 Trigonometric Functions of Any Angle

4.5 Graphs of Sine and Cosine Functions

4.6 Graphs of Other Trigonometric Functions

4.7 Inverse Trigonometric Functions

4.8 Applications and Models

**5. Analytic Trigonometry**

5.1 Using Fundamental Identities

5.2 Verifying Trigonometric Identities

5.3 Solving Trigonometric Equations

5.4 Sum and Difference Formulas

5.5 Multiple-Angle and Product-to-Sum Formulas

**6. Additional Topics in Trigonometry**

6.1 Law of Sines

6.2 Law of Cosines

6.3 Vectors in the Plane

6.4 Vectors and Dot Products

6.5 Trigonometric Form of a Complex Number

**Cumulative Test: Chapters 4-6 Progressive Summary: Chapters 1-6 7. Linear Systems and Matrices**

7.1 Solving Systems of Equations

7.2 Systems of Linear Equations in Two Variables

7.3 Multivariable Linear Systems

7.4 Matrices and Systems of Equations

7.5 Operations with Matrices

7.6 The Inverse of a Square Matrix

7.7 The Determinant of a Square Matrix

7.8 Applications of Matrices and Determinants

**8. Sequences, Series, and Probability**

8.1 Sequence and Series

8.2 Arithmetic Sequences and Partial Sums

8.3 Geometric Sequences and Series

8.4 Mathematical Induction

8.5 The Binomial Theorem

8.6 Counting Principals

8.7 Probability

**Progressive Summary: Chapters 1-8 9. Topics in Analytic Geometry**

9.1 Conics: Circles and Parabolas

9.2 Conics: Ellipses

9.3 Conics: Hyperbolas

9.4 Rotation and Systems of Quadratic Equations

9.5 Parametric Equations

9.6 Polar Coordinates

9.7 Graphs of Polar Equations

9.8 Polar Equations of Conics

**Cumulative Test: Chapters 7-9 10. Analytic Geometry in Three Dimensions**

10.1 The Three-Dimensional Coordinate System

10.2 Vectors in Space

10.3 The Cross Product of Two Vectors

10.4 Lines and Planes in Space

**11. Limits and an Introduction to Calculus**

11.1 Introduction to Limits

11.2 Techniques for Evaluating Limits

11.3 The Tangent Line Problem

11.4 Limits at Infinity and Limits of Sequences

11.5 The Area Problem

**Cumulative Test: Chapters 10-11 Progressive Summary: Chapters 1-11 Appendix A. Technology Support Guide Appendix B. Review of Graphs, Equations, and Inequalities**

B.1 The Cartesian Plane

B.2 Graphs of Equations

B.3 Solving Quadratic Equations Algebraically and Graphically

B.4 Solving Other Equations Algebraically and Graphically

B.5 Solving Inequalities Algebraically and Graphically

B.6 Representing Data Graphically

**Appendix C. Concepts in Statistics**

C.1 Measures of Central Tendency and Dispersion

C.2 Least Squares Regression

**Appendix D. Variation**

D.1 Direct Variation

D.2 Direct Variation as an nth Power

D.3 Inverse Variation

D4 Joint Variation

**Appendix E. Solving Linear Equations and Inequalities Appendix F. Systems of Inequalities**

F.1 Solving Systems of Inequalities

F.2 Linear Programming

Appendix G Study Capsules

Publisher Info

Publisher: Houghton Mifflin Harcourt

Published: 2008

International: No

Published: 2008

International: No

Part of the market-leading Graphing Approach Series by Larson, Hostetler, and Edwards, Precalculus Functions and Graphs: A Graphing Approach, 5/e, is an ideal student and instructor resource for courses that require the use of a graphing calculator. The quality and quantity of the exercises, combined with interesting applications and innovative resources, make teaching easier and help students succeed.

Continuing the series' emphasis on student support, the Fifth Edition introduces Prerequisite Skills Review. For selected examples throughout the text, the Prerequisite Skills Review directs students to previous sections in the text to review concepts and skills needed to master the material at hand. In addition, prerequisite skills review exercises in Eduspace (see below for description) are referenced in every exercise set.

The Larson team achieves accessibility through careful writing and design, including examples with detailed solutions that begin and end on the same page, which maximizes the readability of the text. Similarly, side-by-side solutions show algebraic, graphical, and numerical representations of the mathematics and support a variety of learning styles.

- New! The Nutshell Appendix reviews the essentials of each function, discussed in the Library of Functions feature, and offers study capsules with properties, methods, and examples of the major concepts covered in the textbook. This appendix is an ideal study aid for students.
- New! Progressive Summaries outline newly introduced topics every three chapters and contextualize them within the framework of the course.
- New! Make a Decision exercises--extended modeling applications presented at the end of selected exercise sets--give students the opportunity to apply the mathematical concepts and techniques they've learned to large sets of real data.
- Updated! The Library of Functions, threaded throughout the text, defines each elementary function and its characteristics at first point of use. The Fifth Edition incorporates new exercises that tests students' understanding of these functions. All elementary functions are also presented in a summary on the front endpapers of the text for convenient reference.
- Updated! The Chapter Summaries have been updated to include the Key Terms and Key concepts that are covered in the chapter. These chapter summaries are an effective study aid because they provide a single point of reference for review.
- Updated! The Proofs of Selected Theorems are now presented at the end of each chapter for easy reference.
- The Larson team provides an abundance of features that help students use technology to visualize and understand mathematical concepts. Technology Tips point out the pros and cons of technology use in certain mathematical situations. They also provide alternative methods of solving or checking a problem using a graphing calculator. Students may sometimes be misled by the visuals generated by graphing calculators, so the authors use color to enhance the graphing calculator displays in the textbook, where appropriate. This enables students to visualize concepts accurately and efficiently. Technology Support notes appear throughout the text and refer students to the Technology Support Appendix, where they can learn how to use specific graphing calculator features to enhance their understanding of the concepts presented. The Technology Support notes also direct students to the Graphing Technology Guide, on the textbook's website, for keystroke support for numerous calculator models.
- Carefully positioned throughout the text, Explorations engage students in active discovery of mathematical concepts, strengthening critical thinking skills and helping them to develop an intuitive understanding of theoretical concepts.
- What You Should Learn and Why You Should Learn It appears at the beginning of each chapter and section, offering students a succinct list of the concepts they will soon encounter. Additionally, this feature refers students to an application in the exercise set which helps put the math concept into a real-life context so students can understand it better.
- To help prepare students who intend to move on to Calculus, the authors have placed an icon next to algebraic techniques that are used in Calculus.

**1. Functions and Their Graphs Introduction to Library of Functions**

1.1 Lines in the Plane

1.2 Functions

1.3 Graphs of Functions

1.4 Shifting, Reflection, and Stretching Graphs

1.5 Combinations of Functions

1.6 Inverse Functions

1.7 Linear Models and Scatter Plots

**2. Polynomial and Rational Functions**

2.1 Quadratic Functions

2.2 Polynomial Functions of Higher Degree

2.3 Real Zeros of Polynomial Functions

2.4 Complex Numbers

2.5 The Fundamental Theorem of Algebra

2.6 Rational Functions and Asymptotes

2.7 Graphs of Rational Functions

2.8 Quadratic Models

**Progressive Summary: Chapters 1-2 3. Exponential and Logarithmic Functions**

3.1 Exponential Functions and Their Graphs

3.2 Logarithmic Functions and Their Graphs

3.3 Properties of Logarithms

3.4 Solving Exponential and Logarithmic Equations

3.5 Exponential and Logarithmic Models

3.6 Nonlinear Models

**Cumulative Review: Chapters 1-3 Progressive Summary: Chapters 1-3 4. Trigonometric Functions**

4.1 Radian and Degree Measure

4.2 Trigonometric Functions: The Unit Circle

4.3 Right Triangle Trigonometry

4.4 Trigonometric Functions of Any Angle

4.5 Graphs of Sine and Cosine Functions

4.6 Graphs of Other Trigonometric Functions

4.7 Inverse Trigonometric Functions

4.8 Applications and Models

**5. Analytic Trigonometry**

5.1 Using Fundamental Identities

5.2 Verifying Trigonometric Identities

5.3 Solving Trigonometric Equations

5.4 Sum and Difference Formulas

5.5 Multiple-Angle and Product-to-Sum Formulas

**6. Additional Topics in Trigonometry**

6.1 Law of Sines

6.2 Law of Cosines

6.3 Vectors in the Plane

6.4 Vectors and Dot Products

6.5 Trigonometric Form of a Complex Number

**Cumulative Test: Chapters 4-6 Progressive Summary: Chapters 1-6 7. Linear Systems and Matrices**

7.1 Solving Systems of Equations

7.2 Systems of Linear Equations in Two Variables

7.3 Multivariable Linear Systems

7.4 Matrices and Systems of Equations

7.5 Operations with Matrices

7.6 The Inverse of a Square Matrix

7.7 The Determinant of a Square Matrix

7.8 Applications of Matrices and Determinants

**8. Sequences, Series, and Probability**

8.1 Sequence and Series

8.2 Arithmetic Sequences and Partial Sums

8.3 Geometric Sequences and Series

8.4 Mathematical Induction

8.5 The Binomial Theorem

8.6 Counting Principals

8.7 Probability

**Progressive Summary: Chapters 1-8 9. Topics in Analytic Geometry**

9.1 Conics: Circles and Parabolas

9.2 Conics: Ellipses

9.3 Conics: Hyperbolas

9.4 Rotation and Systems of Quadratic Equations

9.5 Parametric Equations

9.6 Polar Coordinates

9.7 Graphs of Polar Equations

9.8 Polar Equations of Conics

**Cumulative Test: Chapters 7-9 10. Analytic Geometry in Three Dimensions**

10.1 The Three-Dimensional Coordinate System

10.2 Vectors in Space

10.3 The Cross Product of Two Vectors

10.4 Lines and Planes in Space

**11. Limits and an Introduction to Calculus**

11.1 Introduction to Limits

11.2 Techniques for Evaluating Limits

11.3 The Tangent Line Problem

11.4 Limits at Infinity and Limits of Sequences

11.5 The Area Problem

**Cumulative Test: Chapters 10-11 Progressive Summary: Chapters 1-11 Appendix A. Technology Support Guide Appendix B. Review of Graphs, Equations, and Inequalities**

B.1 The Cartesian Plane

B.2 Graphs of Equations

B.3 Solving Quadratic Equations Algebraically and Graphically

B.4 Solving Other Equations Algebraically and Graphically

B.5 Solving Inequalities Algebraically and Graphically

B.6 Representing Data Graphically

**Appendix C. Concepts in Statistics**

C.1 Measures of Central Tendency and Dispersion

C.2 Least Squares Regression

**Appendix D. Variation**

D.1 Direct Variation

D.2 Direct Variation as an nth Power

D.3 Inverse Variation

D4 Joint Variation

**Appendix E. Solving Linear Equations and Inequalities Appendix F. Systems of Inequalities**

F.1 Solving Systems of Inequalities

F.2 Linear Programming

Appendix G Study Capsules