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by Richard N. Aufmann, Joanne Lockwood and Laurie Boswell

Edition: 04Copyright: 2004

Publisher: Houghton Mifflin Harcourt

Published: 2004

International: No

Richard N. Aufmann, Joanne Lockwood and Laurie Boswell

Edition: 04
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Intended for a first-year level developmental mathematics course in intermediate algebra, Exploring Intermediate Algebra: A Graphing Approach is designed to assist students in making connections between mathematics and its applications. Its goal is to develop a student's mathematical skills through appropriate use of applications and to use technology to establish links between abstract mathematical concepts and visual or concrete representations.

- The proven Aufmann Interactive Method (AIM) ensures that students try concepts and manipulate real-life data as they progress through the material. Every objective contains one or more sets of matched-pair examples encouraging students to interact with the text. The first example in each set is completely worked out; the second example, called 'You Try It,' prompts students to practice concepts at the time they are presented in the text. Complete worked-out solutions to these examples in an appendix at the end of the book help students by providing immediate feedback, concept reinforcement, and identification of mistakes to prevent frustration.
- Technology is integrated throughout the text to assist students in making connections between abstract mathematical concepts and a concrete representation provided by technology. This is one way in which students are encouraged to think about and use multiple representations of a concept. The inclusion of technology also facilitates computation in order to focus on analysis rather than manipulation and enables students to examine concepts that would be too difficult or time consuming if the technology were not available.
- Calculator Notes throughout offer tips on using the graphing calculator and See Appendix B notes in student text margin refer students to the graphing calculator appendix for detailed TI-83 and TI-83+ keystroke information.
- AIM for Success, a special preface designed to promote student success, provides students with strategies for using the text and the Aufmann Interactive Method. Suggestions for using this section as a lesson are featured in the Instructor's Resource Manual and the lesson is also available as a PowerPoint presentation.
- Carefully developed approach to problem solving encourages students to develop their own strategies--such as drawing diagrams or writing out the solution steps in words--as part of their solution to a problem. In each case, model solutions encourage students to "State the goal, devise a strategy, solve the problem, and check your work."
- To address different learning styles, a unique side-by-side, multiple approach formatpresents worked-out examples in a two-column layout, with both algebraic and graphical solutions (in either order) that help students make the connection between concepts and concrete representations of the math.
- Applications and real data, selected to motivate an interest in mathematics, require students to use problem-solving strategies along with the skills covered in the section. Applications are taken from many disciplines including agriculture, business, carpentry, chemistry, construction, earth science, education, manufacturing, nutrition, real estate, and sociology. Real data examples and exercises ask students to analyze and solve problems taken from actual situations.
- For ease of navigation, icons identify writing, data, web, and group exercises. In addition, web, CD, video/DVD, and Student Solutions Manual icons at the beginning of each section refer students to relevant supplements. A transparency icon in the Instructor's Annotated Edition denotes figures in the text with transparency masters.
- Chapter Openers clearly orient students to the content with a list of sections in the chapter and a photo and caption that refer to a corresponding example, exercise, or exploration.
- Prep Tests at the beginning of each chapter highlight the prerequisite skills in the upcoming chapter. The answers to these questions can be found in the Answer Appendix along with a reference to the previous section from which the question was taken, encouraging students to review as necessary. Answers to the Prep Test can be found on the same page in Instructor's Annotated Edition. The Go Figure problem that follows the Prep Test is a puzzle problem for interested students.
- Point of Interest student margin notes include an interesting and/or historical sidenote to the math presented.
- Take Note boxes in the student text margin alert students to more complex procedures or remind them to check their work.
- Each section exercise set includes Topics for Discussion, which ask students to discuss or write about a concept; Applying Concepts, which require analysis or offer challenge problems; Explorations, which expand upon a concept presented in the section and are useful in cooperative learning situations or as extra credit assignments; and Real Data Applications, taken from a variety of disciplines and labeled accordingly, which ask students to analyze and solve real-world problems.
- End of chapter material designed to promote success includes Chapter Summaries, with referenced Key Terms and Essential Concepts; Chapter Review Exercises; Chapter Tests; and Cumulative Review Exercises.
- An Instructor's Annotated Edition features Instructor Notes, with teaching ideas, warnings about common student errors, and historical notes. Instructor Notes next to each Example refer teachers to a similar problem in the following exercise set for possible use as an additional in-class example. Suggested Activities (found in the margin) can be used in class to explore concepts, as alternative (discovery) strategies for teaching the concept, or as cooperative learning activities. Suggested Assignments before each exercise set save instructors class preparation time.

**1. Fundamental Concepts**

Section 1.1 Problem Solving

Section 1.2 Sets

Section 1.3 Evaluating Variable Expressions Using Integers

Section 1.4 Evaluating Variable Expressions Using Rational Numbers

Section 1.5 Simplifying Variable Expressions

**2. Introduction to Functions and Relations**

Section 2.1 Rectangular Coordinates and Graphs

Section 2.2 Relations and Functions

Section 2.3 Properties of Functions

**3. First-Degree Equations and Inequalities**

Section 3.1 Solving First-Degree Equations

Section 3.2 Applications of First-Degree Equations

Section 3.3 Applications to Geometry

Section 3.4 Inequalities in One Variable

Section 3.5 Absolute Value Equations and Inequalities

**4. Linear Functions**

Section 4.1 Slopes and Graphs of Linear Functions

Section 4.2 Finding Equations of Straight Lines

Section 4.3 Linear Regression

Section 4.4 Linear Inequalities in Two Variables

**5. Systems of Linear Equations and Inequalities**

Section 5.1 Solving Systems of Linear Equations by Graphing and by the Substitution Method

Section 5.2 Solving Systems of Linear Equations by the Addition Method

Section 5.3 Solving Systems of Linear Equations Using Matrices

Section 5.4 Systems of Linear Inequalities and Linear Programming

**6. Polynomials**

Section 6.1 Operations on Monomials and Scientific Notation

Section 6.2 Addition and Subtraction of Polynomials

Section 6.3 Multiplication and Division of Polynomials

Section 6.4 Factoring Polynomials

Section 6.5 Special Factoring

Section 6.6 Solving Equations by Factoring

**7. Rational Expressions and Equations**

Section 7.1 Introduction to Rational Expressions

Section 7.2 Operations on Rational Expressions

Section 7.3 Rational Equations

Section 7.4 Proportions and Similar Triangles

Section 7.5 Variation

**8. Radical Expressions and Rational Exponents**

Section 8.1 Rational Exponents and Radical Expressions

Section 8.2 Simplifying Radical Expressions

Section 8.3 The Pythagorean Theorem

Section 8.4 Operations on Radical Expressions

Section 8.5 Radical Functions

Section 8.6 Solving Radical Equations

Section 8.7 Complex Numbers

**9. Quadratic Functions and Quadratic Inequalities**

Section 9.1 Introduction to Quadratic Equations

Section 9.2 Solving Quadratic Equations by Taking Square Roots and by Completing the Square

Section 9.3 Solving Quadratic Equations by Using the Quadratic Formula and by Graphing

Section 9.4 Equations That Are Quadratic in Form

Section 9.5 Quadratic Functions

Section 9.6 Quadratic Inequalities

**10. Exponential and Logarithmic Functions**

Section 10.1 Algebra of Functions

Section 10.2 Inverse Functions

Section 10.3 Exponential Functions

Section 10.4 Exponential Models and Exponential Regression

Section 10.5 Logarithmic Functions

Section 10.6 Properties of Logarithms

Section 10.7 Exponential and Logarithmic Equations

**Additional Topics in Algebra**

Section 1 Introduction to Sequences and Series

Section 2 Binomial Expansions

Section 3 Conic Sections

Appendix A. Keystroke Guide for the TI-83 and TI-83 Plus

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Summary

Intended for a first-year level developmental mathematics course in intermediate algebra, Exploring Intermediate Algebra: A Graphing Approach is designed to assist students in making connections between mathematics and its applications. Its goal is to develop a student's mathematical skills through appropriate use of applications and to use technology to establish links between abstract mathematical concepts and visual or concrete representations.

- The proven Aufmann Interactive Method (AIM) ensures that students try concepts and manipulate real-life data as they progress through the material. Every objective contains one or more sets of matched-pair examples encouraging students to interact with the text. The first example in each set is completely worked out; the second example, called 'You Try It,' prompts students to practice concepts at the time they are presented in the text. Complete worked-out solutions to these examples in an appendix at the end of the book help students by providing immediate feedback, concept reinforcement, and identification of mistakes to prevent frustration.
- Technology is integrated throughout the text to assist students in making connections between abstract mathematical concepts and a concrete representation provided by technology. This is one way in which students are encouraged to think about and use multiple representations of a concept. The inclusion of technology also facilitates computation in order to focus on analysis rather than manipulation and enables students to examine concepts that would be too difficult or time consuming if the technology were not available.
- Calculator Notes throughout offer tips on using the graphing calculator and See Appendix B notes in student text margin refer students to the graphing calculator appendix for detailed TI-83 and TI-83+ keystroke information.
- AIM for Success, a special preface designed to promote student success, provides students with strategies for using the text and the Aufmann Interactive Method. Suggestions for using this section as a lesson are featured in the Instructor's Resource Manual and the lesson is also available as a PowerPoint presentation.
- Carefully developed approach to problem solving encourages students to develop their own strategies--such as drawing diagrams or writing out the solution steps in words--as part of their solution to a problem. In each case, model solutions encourage students to "State the goal, devise a strategy, solve the problem, and check your work."
- To address different learning styles, a unique side-by-side, multiple approach formatpresents worked-out examples in a two-column layout, with both algebraic and graphical solutions (in either order) that help students make the connection between concepts and concrete representations of the math.
- Applications and real data, selected to motivate an interest in mathematics, require students to use problem-solving strategies along with the skills covered in the section. Applications are taken from many disciplines including agriculture, business, carpentry, chemistry, construction, earth science, education, manufacturing, nutrition, real estate, and sociology. Real data examples and exercises ask students to analyze and solve problems taken from actual situations.
- For ease of navigation, icons identify writing, data, web, and group exercises. In addition, web, CD, video/DVD, and Student Solutions Manual icons at the beginning of each section refer students to relevant supplements. A transparency icon in the Instructor's Annotated Edition denotes figures in the text with transparency masters.
- Chapter Openers clearly orient students to the content with a list of sections in the chapter and a photo and caption that refer to a corresponding example, exercise, or exploration.
- Prep Tests at the beginning of each chapter highlight the prerequisite skills in the upcoming chapter. The answers to these questions can be found in the Answer Appendix along with a reference to the previous section from which the question was taken, encouraging students to review as necessary. Answers to the Prep Test can be found on the same page in Instructor's Annotated Edition. The Go Figure problem that follows the Prep Test is a puzzle problem for interested students.
- Point of Interest student margin notes include an interesting and/or historical sidenote to the math presented.
- Take Note boxes in the student text margin alert students to more complex procedures or remind them to check their work.
- Each section exercise set includes Topics for Discussion, which ask students to discuss or write about a concept; Applying Concepts, which require analysis or offer challenge problems; Explorations, which expand upon a concept presented in the section and are useful in cooperative learning situations or as extra credit assignments; and Real Data Applications, taken from a variety of disciplines and labeled accordingly, which ask students to analyze and solve real-world problems.
- End of chapter material designed to promote success includes Chapter Summaries, with referenced Key Terms and Essential Concepts; Chapter Review Exercises; Chapter Tests; and Cumulative Review Exercises.
- An Instructor's Annotated Edition features Instructor Notes, with teaching ideas, warnings about common student errors, and historical notes. Instructor Notes next to each Example refer teachers to a similar problem in the following exercise set for possible use as an additional in-class example. Suggested Activities (found in the margin) can be used in class to explore concepts, as alternative (discovery) strategies for teaching the concept, or as cooperative learning activities. Suggested Assignments before each exercise set save instructors class preparation time.

Table of Contents

**1. Fundamental Concepts**

Section 1.1 Problem Solving

Section 1.2 Sets

Section 1.3 Evaluating Variable Expressions Using Integers

Section 1.4 Evaluating Variable Expressions Using Rational Numbers

Section 1.5 Simplifying Variable Expressions

**2. Introduction to Functions and Relations**

Section 2.1 Rectangular Coordinates and Graphs

Section 2.2 Relations and Functions

Section 2.3 Properties of Functions

**3. First-Degree Equations and Inequalities**

Section 3.1 Solving First-Degree Equations

Section 3.2 Applications of First-Degree Equations

Section 3.3 Applications to Geometry

Section 3.4 Inequalities in One Variable

Section 3.5 Absolute Value Equations and Inequalities

**4. Linear Functions**

Section 4.1 Slopes and Graphs of Linear Functions

Section 4.2 Finding Equations of Straight Lines

Section 4.3 Linear Regression

Section 4.4 Linear Inequalities in Two Variables

**5. Systems of Linear Equations and Inequalities**

Section 5.1 Solving Systems of Linear Equations by Graphing and by the Substitution Method

Section 5.2 Solving Systems of Linear Equations by the Addition Method

Section 5.3 Solving Systems of Linear Equations Using Matrices

Section 5.4 Systems of Linear Inequalities and Linear Programming

**6. Polynomials**

Section 6.1 Operations on Monomials and Scientific Notation

Section 6.2 Addition and Subtraction of Polynomials

Section 6.3 Multiplication and Division of Polynomials

Section 6.4 Factoring Polynomials

Section 6.5 Special Factoring

Section 6.6 Solving Equations by Factoring

**7. Rational Expressions and Equations**

Section 7.1 Introduction to Rational Expressions

Section 7.2 Operations on Rational Expressions

Section 7.3 Rational Equations

Section 7.4 Proportions and Similar Triangles

Section 7.5 Variation

**8. Radical Expressions and Rational Exponents**

Section 8.1 Rational Exponents and Radical Expressions

Section 8.2 Simplifying Radical Expressions

Section 8.3 The Pythagorean Theorem

Section 8.4 Operations on Radical Expressions

Section 8.5 Radical Functions

Section 8.6 Solving Radical Equations

Section 8.7 Complex Numbers

**9. Quadratic Functions and Quadratic Inequalities**

Section 9.1 Introduction to Quadratic Equations

Section 9.2 Solving Quadratic Equations by Taking Square Roots and by Completing the Square

Section 9.3 Solving Quadratic Equations by Using the Quadratic Formula and by Graphing

Section 9.4 Equations That Are Quadratic in Form

Section 9.5 Quadratic Functions

Section 9.6 Quadratic Inequalities

**10. Exponential and Logarithmic Functions**

Section 10.1 Algebra of Functions

Section 10.2 Inverse Functions

Section 10.3 Exponential Functions

Section 10.4 Exponential Models and Exponential Regression

Section 10.5 Logarithmic Functions

Section 10.6 Properties of Logarithms

Section 10.7 Exponential and Logarithmic Equations

**Additional Topics in Algebra**

Section 1 Introduction to Sequences and Series

Section 2 Binomial Expansions

Section 3 Conic Sections

Appendix A. Keystroke Guide for the TI-83 and TI-83 Plus

Publisher Info

Publisher: Houghton Mifflin Harcourt

Published: 2004

International: No

Published: 2004

International: No

Intended for a first-year level developmental mathematics course in intermediate algebra, Exploring Intermediate Algebra: A Graphing Approach is designed to assist students in making connections between mathematics and its applications. Its goal is to develop a student's mathematical skills through appropriate use of applications and to use technology to establish links between abstract mathematical concepts and visual or concrete representations.

- The proven Aufmann Interactive Method (AIM) ensures that students try concepts and manipulate real-life data as they progress through the material. Every objective contains one or more sets of matched-pair examples encouraging students to interact with the text. The first example in each set is completely worked out; the second example, called 'You Try It,' prompts students to practice concepts at the time they are presented in the text. Complete worked-out solutions to these examples in an appendix at the end of the book help students by providing immediate feedback, concept reinforcement, and identification of mistakes to prevent frustration.
- Technology is integrated throughout the text to assist students in making connections between abstract mathematical concepts and a concrete representation provided by technology. This is one way in which students are encouraged to think about and use multiple representations of a concept. The inclusion of technology also facilitates computation in order to focus on analysis rather than manipulation and enables students to examine concepts that would be too difficult or time consuming if the technology were not available.
- Calculator Notes throughout offer tips on using the graphing calculator and See Appendix B notes in student text margin refer students to the graphing calculator appendix for detailed TI-83 and TI-83+ keystroke information.
- AIM for Success, a special preface designed to promote student success, provides students with strategies for using the text and the Aufmann Interactive Method. Suggestions for using this section as a lesson are featured in the Instructor's Resource Manual and the lesson is also available as a PowerPoint presentation.
- Carefully developed approach to problem solving encourages students to develop their own strategies--such as drawing diagrams or writing out the solution steps in words--as part of their solution to a problem. In each case, model solutions encourage students to "State the goal, devise a strategy, solve the problem, and check your work."
- To address different learning styles, a unique side-by-side, multiple approach formatpresents worked-out examples in a two-column layout, with both algebraic and graphical solutions (in either order) that help students make the connection between concepts and concrete representations of the math.
- Applications and real data, selected to motivate an interest in mathematics, require students to use problem-solving strategies along with the skills covered in the section. Applications are taken from many disciplines including agriculture, business, carpentry, chemistry, construction, earth science, education, manufacturing, nutrition, real estate, and sociology. Real data examples and exercises ask students to analyze and solve problems taken from actual situations.
- For ease of navigation, icons identify writing, data, web, and group exercises. In addition, web, CD, video/DVD, and Student Solutions Manual icons at the beginning of each section refer students to relevant supplements. A transparency icon in the Instructor's Annotated Edition denotes figures in the text with transparency masters.
- Chapter Openers clearly orient students to the content with a list of sections in the chapter and a photo and caption that refer to a corresponding example, exercise, or exploration.
- Prep Tests at the beginning of each chapter highlight the prerequisite skills in the upcoming chapter. The answers to these questions can be found in the Answer Appendix along with a reference to the previous section from which the question was taken, encouraging students to review as necessary. Answers to the Prep Test can be found on the same page in Instructor's Annotated Edition. The Go Figure problem that follows the Prep Test is a puzzle problem for interested students.
- Point of Interest student margin notes include an interesting and/or historical sidenote to the math presented.
- Take Note boxes in the student text margin alert students to more complex procedures or remind them to check their work.
- Each section exercise set includes Topics for Discussion, which ask students to discuss or write about a concept; Applying Concepts, which require analysis or offer challenge problems; Explorations, which expand upon a concept presented in the section and are useful in cooperative learning situations or as extra credit assignments; and Real Data Applications, taken from a variety of disciplines and labeled accordingly, which ask students to analyze and solve real-world problems.
- End of chapter material designed to promote success includes Chapter Summaries, with referenced Key Terms and Essential Concepts; Chapter Review Exercises; Chapter Tests; and Cumulative Review Exercises.
- An Instructor's Annotated Edition features Instructor Notes, with teaching ideas, warnings about common student errors, and historical notes. Instructor Notes next to each Example refer teachers to a similar problem in the following exercise set for possible use as an additional in-class example. Suggested Activities (found in the margin) can be used in class to explore concepts, as alternative (discovery) strategies for teaching the concept, or as cooperative learning activities. Suggested Assignments before each exercise set save instructors class preparation time.

**1. Fundamental Concepts**

Section 1.1 Problem Solving

Section 1.2 Sets

Section 1.3 Evaluating Variable Expressions Using Integers

Section 1.4 Evaluating Variable Expressions Using Rational Numbers

Section 1.5 Simplifying Variable Expressions

**2. Introduction to Functions and Relations**

Section 2.1 Rectangular Coordinates and Graphs

Section 2.2 Relations and Functions

Section 2.3 Properties of Functions

**3. First-Degree Equations and Inequalities**

Section 3.1 Solving First-Degree Equations

Section 3.2 Applications of First-Degree Equations

Section 3.3 Applications to Geometry

Section 3.4 Inequalities in One Variable

Section 3.5 Absolute Value Equations and Inequalities

**4. Linear Functions**

Section 4.1 Slopes and Graphs of Linear Functions

Section 4.2 Finding Equations of Straight Lines

Section 4.3 Linear Regression

Section 4.4 Linear Inequalities in Two Variables

**5. Systems of Linear Equations and Inequalities**

Section 5.1 Solving Systems of Linear Equations by Graphing and by the Substitution Method

Section 5.2 Solving Systems of Linear Equations by the Addition Method

Section 5.3 Solving Systems of Linear Equations Using Matrices

Section 5.4 Systems of Linear Inequalities and Linear Programming

**6. Polynomials**

Section 6.1 Operations on Monomials and Scientific Notation

Section 6.2 Addition and Subtraction of Polynomials

Section 6.3 Multiplication and Division of Polynomials

Section 6.4 Factoring Polynomials

Section 6.5 Special Factoring

Section 6.6 Solving Equations by Factoring

**7. Rational Expressions and Equations**

Section 7.1 Introduction to Rational Expressions

Section 7.2 Operations on Rational Expressions

Section 7.3 Rational Equations

Section 7.4 Proportions and Similar Triangles

Section 7.5 Variation

**8. Radical Expressions and Rational Exponents**

Section 8.1 Rational Exponents and Radical Expressions

Section 8.2 Simplifying Radical Expressions

Section 8.3 The Pythagorean Theorem

Section 8.4 Operations on Radical Expressions

Section 8.5 Radical Functions

Section 8.6 Solving Radical Equations

Section 8.7 Complex Numbers

**9. Quadratic Functions and Quadratic Inequalities**

Section 9.1 Introduction to Quadratic Equations

Section 9.2 Solving Quadratic Equations by Taking Square Roots and by Completing the Square

Section 9.3 Solving Quadratic Equations by Using the Quadratic Formula and by Graphing

Section 9.4 Equations That Are Quadratic in Form

Section 9.5 Quadratic Functions

Section 9.6 Quadratic Inequalities

**10. Exponential and Logarithmic Functions**

Section 10.1 Algebra of Functions

Section 10.2 Inverse Functions

Section 10.3 Exponential Functions

Section 10.4 Exponential Models and Exponential Regression

Section 10.5 Logarithmic Functions

Section 10.6 Properties of Logarithms

Section 10.7 Exponential and Logarithmic Equations

**Additional Topics in Algebra**

Section 1 Introduction to Sequences and Series

Section 2 Binomial Expansions

Section 3 Conic Sections

Appendix A. Keystroke Guide for the TI-83 and TI-83 Plus