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by Ron Larson

Cover type: HardbackEdition: 4TH 05

Copyright: 2005

Publisher: Houghton Mifflin Harcourt

Published: 2005

International: No

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As part of the market-leading Graphing Approach Series by Larson, Hostetler, and Edwards, Precalculus with Limits: A Graphing Approach, 4/e, provides both students and instructors with a sound mathematics course in an approachable, understandable format. The quality and quantity of the exercises, combined with interesting applications, cutting-edge design, and innovative resources, make teaching easier and help students succeed in mathematics. This new edition, intended for precalculus courses that require the use of a graphing calculator, includes a moderate review of algebra to help students entering the course with weak algebra skills.

- Enhanced accessibility to students is achieved through careful writing and design, including same-page examples and solutions, which maximize the readability of the text. Similarly, side-by-side solutions show algebraic, visual, and numeric representations of the mathematics to support students' various learning styles.
- New! The Library of Functions thread throughout the text provides a definition and list of characteristics for each elementary function and compares newly introduced functions to those already presented to increase students' understanding of these important concepts. A Library of Functions Summary also appears inside the front cover for quick reference.
- New! Technology Support notes provided at point-of-use throughout the text guide 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. These notes also direct students to the Graphing Technology Guide on the textbook web site for keystroke support.
- New! Technology Tips, also provided at point-of-use, call attention to the strengths and weaknesses of graphing technology. Some of these tips offer alternative methods for solving or checking a problem using technology.
- New! Because students are often misled by the jagged nature of graphs generated by graphing calculators, this text frequently highlights the path of a function in color on the calculator image. This unique design feature enables students to visualize the mathematical concepts clearly and accurately and avoid common misunderstandings.
- Study Tips at point-of-use throughout the text reinforce concepts and help students learn how to study mathematics.
- New! Checkpoint questions appear after each worked-out solution, directing students to work a similar exercise for further practice or concept reinforcement. These can be used by instructors in class to quickly check student understanding or by students to practice and study concepts.
- Chapter Review exercises, Chapter Tests, and periodic Cumulative Tests offer students frequent opportunities for self-assessment and help them to develop strong study- and test-taking skills.
- The Student Success Organizer is a valuable note-taking guide that helps students organize their class notes and create an effective study and review tool.
- New! Text-specific Tutorial Support is provided in numerous additional resources designed to help students succeed. These resources include live online tutoring, instructional DVDs and videos, and algorithmic tutorial support and self-assessment available on CD-ROM and the web.
- Explorations provided at point-of-use throughout the text can help instructors provide a quick introduction to concepts or reinforce student understanding.
- Modeling Exercises are integrated throughout the text to motivate students and allow them to see the usefulness of the concepts being presented.
- Assignments are easily customized to the difficulty level of the instructor's choice. Exercises are carefully graded in difficulty from mastery of basic skills to more challenging. For example, Review Exercises in each section reinforce previously learned skills in preparation for the next lesson. Synthesis Exercises combine skills and check for conceptual understanding. For those instructors wanting to incorporate more theory, Proofs in Mathematics, allowing instructors to incorporate more theory, are provided for selected theorems in Appendix B.
- A variety of exercise types is included in each exercise set. Questions involving skills, writing, critical thinking, problem solving, applications, and real data sets are included throughout the text. Exercises are presented in a variety of question formats, including free response, true/false, and fill-in the blank.
- New! Vocabulary questions at the beginning of every exercise set help students learn proper mathematical terminology.
- New! Houghton Mifflin's Eduspace online classroom management tool offers instructors the option to assign homework and tests online, provides tutorial support for students needing additional help, and includes the ability to grade any of these assignments automatically.
- New! Digital Lessons and Digital Figures in PowerPoint provide instructors editable electronic instructional resources. These pre-created lessons and textbook figures make it easier than ever for instructors to present in-class examples and graphics. In addition, for instructors with limited office hours, the full-color presentation helps promote better understanding among students, who can access these slides online to review lectures and prepare for exams.
- The Instructor Success Organizer includes suggested lesson plans for each section of the text and is an especially useful tool for larger departments that want all sections of a course to follow the same outline.
- The Instructor's Edition of the Student Success Organizer can serve as a lecture outline for every section of the text and includes additional examples for classroom discussion. This is another valuable resource for schools promoting consistent instruction or to support less-experienced instructors.

**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, Reflecting, and Stretching Graphs

1.5 Combinations of Functions

1.6 Inverse Functions

1.7 Exploring Data: 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 Exploring Data: Quadratic Models

**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 Exploring Data: Nonlinear Models

Cumulative Test: Chapters 1-3

**4. Trigonometric Functions**

4.1 Radian and Degree Measure

4.2 Trigonmetric 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-Anlge 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

**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 Sequences 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 Principles

8.7 Probability

**9. Topics in Analytic Geometry**

9.1 Introduction to Conics: Parabolas

9.2 Ellipses

9.3 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

Appendix A Technology Support

Appendix B Review of Graphs, Equations, and Inequalities

B.1 The Cartesian Plane

B.2 Graphs of Equations

B.3 Solving Equations Algebraically and Graphically

B.4 Solving Inequalities Algebraically and Graphically

B.5 Exploring Data: Representing Data Graphically

Appendix C Proofs of Selected Theorems

Appendix D Concepts in Statistics

D.1 Measures of Central Tendency and Dispersion

D.2 Least Squares Regression

Appendix E Solving Linear Equations and Inequalities

Appendix F Systems of Inequalities

F.1 Solving Systems of Inequalities

F.2 Linear Programming

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Summary

As part of the market-leading Graphing Approach Series by Larson, Hostetler, and Edwards, Precalculus with Limits: A Graphing Approach, 4/e, provides both students and instructors with a sound mathematics course in an approachable, understandable format. The quality and quantity of the exercises, combined with interesting applications, cutting-edge design, and innovative resources, make teaching easier and help students succeed in mathematics. This new edition, intended for precalculus courses that require the use of a graphing calculator, includes a moderate review of algebra to help students entering the course with weak algebra skills.

- Enhanced accessibility to students is achieved through careful writing and design, including same-page examples and solutions, which maximize the readability of the text. Similarly, side-by-side solutions show algebraic, visual, and numeric representations of the mathematics to support students' various learning styles.
- New! The Library of Functions thread throughout the text provides a definition and list of characteristics for each elementary function and compares newly introduced functions to those already presented to increase students' understanding of these important concepts. A Library of Functions Summary also appears inside the front cover for quick reference.
- New! Technology Support notes provided at point-of-use throughout the text guide 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. These notes also direct students to the Graphing Technology Guide on the textbook web site for keystroke support.
- New! Technology Tips, also provided at point-of-use, call attention to the strengths and weaknesses of graphing technology. Some of these tips offer alternative methods for solving or checking a problem using technology.
- New! Because students are often misled by the jagged nature of graphs generated by graphing calculators, this text frequently highlights the path of a function in color on the calculator image. This unique design feature enables students to visualize the mathematical concepts clearly and accurately and avoid common misunderstandings.
- Study Tips at point-of-use throughout the text reinforce concepts and help students learn how to study mathematics.
- New! Checkpoint questions appear after each worked-out solution, directing students to work a similar exercise for further practice or concept reinforcement. These can be used by instructors in class to quickly check student understanding or by students to practice and study concepts.
- Chapter Review exercises, Chapter Tests, and periodic Cumulative Tests offer students frequent opportunities for self-assessment and help them to develop strong study- and test-taking skills.
- The Student Success Organizer is a valuable note-taking guide that helps students organize their class notes and create an effective study and review tool.
- New! Text-specific Tutorial Support is provided in numerous additional resources designed to help students succeed. These resources include live online tutoring, instructional DVDs and videos, and algorithmic tutorial support and self-assessment available on CD-ROM and the web.
- Explorations provided at point-of-use throughout the text can help instructors provide a quick introduction to concepts or reinforce student understanding.
- Modeling Exercises are integrated throughout the text to motivate students and allow them to see the usefulness of the concepts being presented.
- Assignments are easily customized to the difficulty level of the instructor's choice. Exercises are carefully graded in difficulty from mastery of basic skills to more challenging. For example, Review Exercises in each section reinforce previously learned skills in preparation for the next lesson. Synthesis Exercises combine skills and check for conceptual understanding. For those instructors wanting to incorporate more theory, Proofs in Mathematics, allowing instructors to incorporate more theory, are provided for selected theorems in Appendix B.
- A variety of exercise types is included in each exercise set. Questions involving skills, writing, critical thinking, problem solving, applications, and real data sets are included throughout the text. Exercises are presented in a variety of question formats, including free response, true/false, and fill-in the blank.
- New! Vocabulary questions at the beginning of every exercise set help students learn proper mathematical terminology.
- New! Houghton Mifflin's Eduspace online classroom management tool offers instructors the option to assign homework and tests online, provides tutorial support for students needing additional help, and includes the ability to grade any of these assignments automatically.
- New! Digital Lessons and Digital Figures in PowerPoint provide instructors editable electronic instructional resources. These pre-created lessons and textbook figures make it easier than ever for instructors to present in-class examples and graphics. In addition, for instructors with limited office hours, the full-color presentation helps promote better understanding among students, who can access these slides online to review lectures and prepare for exams.
- The Instructor Success Organizer includes suggested lesson plans for each section of the text and is an especially useful tool for larger departments that want all sections of a course to follow the same outline.
- The Instructor's Edition of the Student Success Organizer can serve as a lecture outline for every section of the text and includes additional examples for classroom discussion. This is another valuable resource for schools promoting consistent instruction or to support less-experienced instructors.

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, Reflecting, and Stretching Graphs

1.5 Combinations of Functions

1.6 Inverse Functions

1.7 Exploring Data: 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 Exploring Data: Quadratic Models

**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 Exploring Data: Nonlinear Models

Cumulative Test: Chapters 1-3

**4. Trigonometric Functions**

4.1 Radian and Degree Measure

4.2 Trigonmetric 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-Anlge 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

**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 Sequences 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 Principles

8.7 Probability

**9. Topics in Analytic Geometry**

9.1 Introduction to Conics: Parabolas

9.2 Ellipses

9.3 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

Appendix A Technology Support

Appendix B Review of Graphs, Equations, and Inequalities

B.1 The Cartesian Plane

B.2 Graphs of Equations

B.3 Solving Equations Algebraically and Graphically

B.4 Solving Inequalities Algebraically and Graphically

B.5 Exploring Data: Representing Data Graphically

Appendix C Proofs of Selected Theorems

Appendix D Concepts in Statistics

D.1 Measures of Central Tendency and Dispersion

D.2 Least Squares Regression

Appendix E Solving Linear Equations and Inequalities

Appendix F Systems of Inequalities

F.1 Solving Systems of Inequalities

F.2 Linear Programming

Publisher Info

Publisher: Houghton Mifflin Harcourt

Published: 2005

International: No

Published: 2005

International: No

As part of the market-leading Graphing Approach Series by Larson, Hostetler, and Edwards, Precalculus with Limits: A Graphing Approach, 4/e, provides both students and instructors with a sound mathematics course in an approachable, understandable format. The quality and quantity of the exercises, combined with interesting applications, cutting-edge design, and innovative resources, make teaching easier and help students succeed in mathematics. This new edition, intended for precalculus courses that require the use of a graphing calculator, includes a moderate review of algebra to help students entering the course with weak algebra skills.

- Enhanced accessibility to students is achieved through careful writing and design, including same-page examples and solutions, which maximize the readability of the text. Similarly, side-by-side solutions show algebraic, visual, and numeric representations of the mathematics to support students' various learning styles.
- New! The Library of Functions thread throughout the text provides a definition and list of characteristics for each elementary function and compares newly introduced functions to those already presented to increase students' understanding of these important concepts. A Library of Functions Summary also appears inside the front cover for quick reference.
- New! Technology Support notes provided at point-of-use throughout the text guide 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. These notes also direct students to the Graphing Technology Guide on the textbook web site for keystroke support.
- New! Technology Tips, also provided at point-of-use, call attention to the strengths and weaknesses of graphing technology. Some of these tips offer alternative methods for solving or checking a problem using technology.
- New! Because students are often misled by the jagged nature of graphs generated by graphing calculators, this text frequently highlights the path of a function in color on the calculator image. This unique design feature enables students to visualize the mathematical concepts clearly and accurately and avoid common misunderstandings.
- Study Tips at point-of-use throughout the text reinforce concepts and help students learn how to study mathematics.
- New! Checkpoint questions appear after each worked-out solution, directing students to work a similar exercise for further practice or concept reinforcement. These can be used by instructors in class to quickly check student understanding or by students to practice and study concepts.
- Chapter Review exercises, Chapter Tests, and periodic Cumulative Tests offer students frequent opportunities for self-assessment and help them to develop strong study- and test-taking skills.
- The Student Success Organizer is a valuable note-taking guide that helps students organize their class notes and create an effective study and review tool.
- New! Text-specific Tutorial Support is provided in numerous additional resources designed to help students succeed. These resources include live online tutoring, instructional DVDs and videos, and algorithmic tutorial support and self-assessment available on CD-ROM and the web.
- Explorations provided at point-of-use throughout the text can help instructors provide a quick introduction to concepts or reinforce student understanding.
- Modeling Exercises are integrated throughout the text to motivate students and allow them to see the usefulness of the concepts being presented.
- Assignments are easily customized to the difficulty level of the instructor's choice. Exercises are carefully graded in difficulty from mastery of basic skills to more challenging. For example, Review Exercises in each section reinforce previously learned skills in preparation for the next lesson. Synthesis Exercises combine skills and check for conceptual understanding. For those instructors wanting to incorporate more theory, Proofs in Mathematics, allowing instructors to incorporate more theory, are provided for selected theorems in Appendix B.
- A variety of exercise types is included in each exercise set. Questions involving skills, writing, critical thinking, problem solving, applications, and real data sets are included throughout the text. Exercises are presented in a variety of question formats, including free response, true/false, and fill-in the blank.
- New! Vocabulary questions at the beginning of every exercise set help students learn proper mathematical terminology.
- New! Houghton Mifflin's Eduspace online classroom management tool offers instructors the option to assign homework and tests online, provides tutorial support for students needing additional help, and includes the ability to grade any of these assignments automatically.
- New! Digital Lessons and Digital Figures in PowerPoint provide instructors editable electronic instructional resources. These pre-created lessons and textbook figures make it easier than ever for instructors to present in-class examples and graphics. In addition, for instructors with limited office hours, the full-color presentation helps promote better understanding among students, who can access these slides online to review lectures and prepare for exams.
- The Instructor Success Organizer includes suggested lesson plans for each section of the text and is an especially useful tool for larger departments that want all sections of a course to follow the same outline.
- The Instructor's Edition of the Student Success Organizer can serve as a lecture outline for every section of the text and includes additional examples for classroom discussion. This is another valuable resource for schools promoting consistent instruction or to support less-experienced instructors.

**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, Reflecting, and Stretching Graphs

1.5 Combinations of Functions

1.6 Inverse Functions

1.7 Exploring Data: 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 Exploring Data: Quadratic Models

**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 Exploring Data: Nonlinear Models

Cumulative Test: Chapters 1-3

**4. Trigonometric Functions**

4.1 Radian and Degree Measure

4.2 Trigonmetric 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-Anlge 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

**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 Sequences 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 Principles

8.7 Probability

**9. Topics in Analytic Geometry**

9.1 Introduction to Conics: Parabolas

9.2 Ellipses

9.3 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

Appendix A Technology Support

Appendix B Review of Graphs, Equations, and Inequalities

B.1 The Cartesian Plane

B.2 Graphs of Equations

B.3 Solving Equations Algebraically and Graphically

B.4 Solving Inequalities Algebraically and Graphically

B.5 Exploring Data: Representing Data Graphically

Appendix C Proofs of Selected Theorems

Appendix D Concepts in Statistics

D.1 Measures of Central Tendency and Dispersion

D.2 Least Squares Regression

Appendix E Solving Linear Equations and Inequalities

Appendix F Systems of Inequalities

F.1 Solving Systems of Inequalities

F.2 Linear Programming