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More About This Textbook
Overview
Product Details
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Meet the Author
An awardwinning instructor and bestselling author, Elayn MartinGay has taught mathematics at the University of New Orleans for more than 25 years. Her numerous teaching awards include the local University Alumni Association’s Award for Excellence in Teaching, and Outstanding Developmental Educator at University of New Orleans, presented by the Louisiana Association of Developmental Educators.
Prior to writing textbooks, Elayn developed an acclaimed series of lecture videos to support developmental mathematics students in their quest for success. These highly successful videos originally served as the foundation material for her texts. Today, the videos are specific to each book in the MartinGay series. Elayn also pioneered the Chapter Test Prep Video to help students as they prepare for a test–their most “teachable moment!”
Elayn’s experience has made her aware of how busy instructors are and what a difference quality support makes. For this reason, she created the InstructortoInstructor video series. These videos provide instructors with suggestions for presenting specific math topics and concepts in basic mathematics, Prealgebra, beginning algebra, and intermediate algebra. Seasoned instructors can use them as a source for alternate approaches in the classroom. New or adjunct faculty may find the CDs useful for review.
Her textbooks and acclaimed video program support Elayn's passion of helping every student to succeed.
Read an Excerpt
PREFACE
ABOUT THIS BOOK
Intermediate Algebra: A Graphing Approach, Second Edition was written to provide a solid foundation in algebra as well as to develop students' problemsolving skills. Specific care has been taken to ensure that students have the most uptodate and relevant text preparation for their next mathematics course, as well as to help students succeed in nonmathematical courses that require a grasp of algebraic fundamentals. We have tried to achieve this by writing a userfriendly text that is keyed to objectives and contains many workedout examples. The basic concepts of graphs and functions are introduced early, and problemsolving techniques, reallife and realdata applications, data interpretation, mental mathematics, number sense, critical thinking, decision making, and geometric concepts are emphasized and integrated throughout the book. This text makes reference to the use of graphing technology to help students better understand important mathematical connections.
The many factors that contributed to the success of the first edition have been retained. In preparing this edition, we considered the comments and suggestions of colleagues throughout the country, students, and users of the prior edition. The AMATYC Crossroads in Mathematics: Standards for Introductory College Mathematics before Calculus and the MAA and NCTM standards (plus Addenda), together with advances in technology, also influenced the writing of this text.
Intermediate Algebra: A Graphing Approach, Second Edition is part of a series of texts that can include Basic College Mathematics,Prealgebra, Third Edition, and Beginning Algebra, Third Edition. Also available are Beginning and Intermediate Algebra, Second Edition, a combined algebra text and Intermediate Algebra, Third Edition. Throughout the series, pedagogical features are designed to develop student proficiency in algebra and problem solving and to prepare students for future courses.
KEY PEDAGOGICAL FEATURES IN THE THIRD EDITION
Readability and Connections. We have tried to make the writing style as clear as possible while still retaining the mathematical integrity of the content. When a new topic is presented, an effort has been made to relate the new ideas to those that students may already know. Constant reinforcement and connections within problemsolving strategies, data interpretation, geometry, patterns, graphs, and situations from everyday life can help students gradually master both new and old information.
Problem Solving Process. This is formally introduced in Chapter 1 with a new fourstep process that is integrated throughout the text. The four steps are Understand, Translate, Solve, and Interpret. The repeated use of these steps throughout the text in a variety of examples shows their wide applicability. Reinforcing the steps can increase students' confidence in beginning problems. When solving problems, students are encouraged to use technology when applicable during this problemsolving process and/or when checking a solution. For instance, with technology, a graph can be generated quickly and accurately in order to enhance the problemsolving process.
Applications and Connections. Every effort was made to include as many accessible, interesting, and relevant reallife applications as possible throughout the text in both workedout examples and exercise sets. The applications strengthen students' understanding of mathematics in the real world and help to motivate them. They show connections to a wide range of fields including agriculture, allied health, art, astronomy, automotive ownership, aviation, biology, business, chemistry, communication, computer technology, construction, consumer affairs, demographics, earth science, education, entertainment, environmental issues, finance and economics, food service, geography, government, history, hobbies, labor and career issues, life science, medicine, music, nutrition, physics, political science, population, recreation, sports, technology, transportation, travel, weather, and important related mathematical areas such as geometry and statistics. (See the Index of Applications on page xxi.) Many of the applications are based on recent and interesting reallife data. For instance, see Section 2.4, exercise 76, Section 4.3, exercise 44 , or Section 5.3 exercise 85, for a variety of ways real data is used. Sources for data include newspapers, magazines, government publications, publicly held companies, special interest groups, research organizations, and reference books. Opportunities for obtaining your own real data with and without using the internet are also included.
Discover the Concept. These explorations, integrated appropriately throughout the text, are often for use with graphing calculators or computer graphing utilities. They promote student involvement and interaction with the text as students are reading. This feature helps students recognize patterns or discover a concept on their own immediately before the concept is formally introduced.
Helpful Hints. Helpful Hints, formerly Reminders, contain practical advice on applying mathematical concepts. These are found throughout the text and strategically placed where students are most likely to need immediate reinforcement. They are highlighted in a box for quick reference and, as appropriate, an indicator line is used to precisely identify the particular part of a problem or concept being discussed. For instance, see pages 129 and 348.
Technology Note. Generally found in the margin, technology notes contain specific suggestions for problem solving with technology. They also contain notes on extra features students might find available on their graphing utilities.
Visual Reinforcement of Concepts. The text contains numerous graphics, models, and illustrations to visually clarify and reinforce concepts. These include new and updated bar graphs and circle graphs in two and three dimensions, line graphs, calculator screens, application illustrations, photographs, and geometric figures. There are now approximately 1,000 figures.
Real World Chapter Openers. The new twopage chapter opener focuses on how math is used in a specific career, provides links to the World Wide Web, and references a "Spotlight on Decision Making" feature within the chapter for further exploration of the career and the relevance of algebra. For example, look at the opener for Chapter 4. The opening pages also contain a list of section titles and an introduction to the mathematics to be studied together with mathematical connections to previous chapters in the text.
Student Resource Icons. At the beginning of each section, videotape, tutorial software CD ROM, Student Solutions Manual, and Study Guide icons are displayed. These icons help remind students that these learning aids are available should they choose to use them to review concepts and skills at their own pace. These items have direct correlation to the text and emphasize the text's methods of solution.
Chapter Highlights. Found at the end of each chapter, the Chapter Highlights contain key definitions, concepts, and examples to help students understand and retain what they have learned.
Chapter Project. This feature occurs at the end of each chapter, often serving as a chapter wrapup. For individual or group completion, the muftipart Chapter Project, usually handson or data based, allows students to problem solve, make interpretations, and to think and write about algebra.
In addition, a reference to alternative or additional Real World Activities is given. This internet option invites students to find and retrieve real data for use in solving problems. Visit the Real World Activities site by going to ...
Table of Contents
Preface
PREFACE
ABOUT THIS BOOK
Intermediate Algebra: A Graphing Approach, Second Edition was written to provide a solid foundation in algebra as well as to develop students' problemsolving skills. Specific care has been taken to ensure that students have the most uptodate and relevant text preparation for their next mathematics course, as well as to help students succeed in nonmathematical courses that require a grasp of algebraic fundamentals. We have tried to achieve this by writing a userfriendly text that is keyed to objectives and contains many workedout examples. The basic concepts of graphs and functions are introduced early, and problemsolving techniques, reallife and realdata applications, data interpretation, mental mathematics, number sense, critical thinking, decision making, and geometric concepts are emphasized and integrated throughout the book. This text makes reference to the use of graphing technology to help students better understand important mathematical connections.
The many factors that contributed to the success of the first edition have been retained. In preparing this edition, we considered the comments and suggestions of colleagues throughout the country, students, and users of the prior edition. The AMATYC Crossroads in Mathematics: Standards for Introductory College Mathematics before Calculus and the MAA and NCTM standards (plus Addenda), together with advances in technology, also influenced the writing of this text.
Intermediate Algebra: A Graphing Approach, Second Edition is part of a series of texts that can include Basic College Mathematics,Prealgebra, Third Edition, and Beginning Algebra, Third Edition. Also available are Beginning and Intermediate Algebra, Second Edition, a combined algebra text and Intermediate Algebra, Third Edition. Throughout the series, pedagogical features are designed to develop student proficiency in algebra and problem solving and to prepare students for future courses.
KEY PEDAGOGICAL FEATURES IN THE THIRD EDITION
Readability and Connections. We have tried to make the writing style as clear as possible while still retaining the mathematical integrity of the content. When a new topic is presented, an effort has been made to relate the new ideas to those that students may already know. Constant reinforcement and connections within problemsolving strategies, data interpretation, geometry, patterns, graphs, and situations from everyday life can help students gradually master both new and old information.
Problem Solving Process. This is formally introduced in Chapter 1 with a new fourstep process that is integrated throughout the text. The four steps are Understand, Translate, Solve, and Interpret. The repeated use of these steps throughout the text in a variety of examples shows their wide applicability. Reinforcing the steps can increase students' confidence in beginning problems. When solving problems, students are encouraged to use technology when applicable during this problemsolving process and/or when checking a solution. For instance, with technology, a graph can be generated quickly and accurately in order to enhance the problemsolving process.
Applications and Connections. Every effort was made to include as many accessible, interesting, and relevant reallife applications as possible throughout the text in both workedout examples and exercise sets. The applications strengthen students' understanding of mathematics in the real world and help to motivate them. They show connections to a wide range of fields including agriculture, allied health, art, astronomy, automotive ownership, aviation, biology, business, chemistry, communication, computer technology, construction, consumer affairs, demographics, earth science, education, entertainment, environmental issues, finance and economics, food service, geography, government, history, hobbies, labor and career issues, life science, medicine, music, nutrition, physics, political science, population, recreation, sports, technology, transportation, travel, weather, and important related mathematical areas such as geometry and statistics. (See the Index of Applications on page xxi.) Many of the applications are based on recent and interesting reallife data. For instance, see Section 2.4, exercise 76, Section 4.3, exercise 44 , or Section 5.3 exercise 85, for a variety of ways real data is used. Sources for data include newspapers, magazines, government publications, publicly held companies, special interest groups, research organizations, and reference books. Opportunities for obtaining your own real data with and without using the internet are also included.
Discover the Concept. These explorations, integrated appropriately throughout the text, are often for use with graphing calculators or computer graphing utilities. They promote student involvement and interaction with the text as students are reading. This feature helps students recognize patterns or discover a concept on their own immediately before the concept is formally introduced.
Helpful Hints. Helpful Hints, formerly Reminders, contain practical advice on applying mathematical concepts. These are found throughout the text and strategically placed where students are most likely to need immediate reinforcement. They are highlighted in a box for quick reference and, as appropriate, an indicator line is used to precisely identify the particular part of a problem or concept being discussed. For instance, see pages 129 and 348.
Technology Note. Generally found in the margin, technology notes contain specific suggestions for problem solving with technology. They also contain notes on extra features students might find available on their graphing utilities.
Visual Reinforcement of Concepts. The text contains numerous graphics, models, and illustrations to visually clarify and reinforce concepts. These include new and updated bar graphs and circle graphs in two and three dimensions, line graphs, calculator screens, application illustrations, photographs, and geometric figures. There are now approximately 1,000 figures.
Real World Chapter Openers. The new twopage chapter opener focuses on how math is used in a specific career, provides links to the World Wide Web, and references a "Spotlight on Decision Making" feature within the chapter for further exploration of the career and the relevance of algebra. For example, look at the opener for Chapter 4. The opening pages also contain a list of section titles and an introduction to the mathematics to be studied together with mathematical connections to previous chapters in the text.
Student Resource Icons. At the beginning of each section, videotape, tutorial software CD ROM, Student Solutions Manual, and Study Guide icons are displayed. These icons help remind students that these learning aids are available should they choose to use them to review concepts and skills at their own pace. These items have direct correlation to the text and emphasize the text's methods of solution.
Chapter Highlights. Found at the end of each chapter, the Chapter Highlights contain key definitions, concepts, and examples to help students understand and retain what they have learned.
Chapter Project. This feature occurs at the end of each chapter, often serving as a chapter wrapup. For individual or group completion, the muftipart Chapter Project, usually handson or data based, allows students to problem solve, make interpretations, and to think and write about algebra.
In addition, a reference to alternative or additional Real World Activities is given. This internet option invites students to find and retrieve real data for use in solving problems. Visit the Real World Activities site by going to http://www.prenhall.com/martingay.
Functional Use of Color and New Design. Elements of this text are highlighted with color or design to make it easier for students to read and study. Special care has been taken to use color within solutions to examples or in the art to help clarify, distinguish, or connect concepts. For example, look at page 555 in Section 8.5.
EXERCISE SETS
Each text section ends with an exercise set, usually divided into two parts. Both parts contain graded exercises. The first part is carefully keyed to at least one worked example in the text. Once a student has gained confidence in a skill, the second part contains exercises not keyed to examples.
Throughout the text exercises there is an emphasis on data and graphical interpretation via tables, charts, and graphs. The ability to interpret data and read and create a variety of types of graphs is developed gradually so students become comfortable with it. Similarly, throughout the text there is integration of geometric concepts, such as perimeter and area. Exercises and examples marked with a geometry icon have been identified for convenience.
Each exercise set contains one or more of the following features.
Spotlight on Decision Making. These unique new, specially designed applications help students develop their decisionmaking and problemsolving abilities, skills useful in mathematics and in life. Appropriately placed before an exercise set begins, students have an opportunity to immediately practice and reinforce basic algebraic concepts found in the accompanying section in relevant, accessible contexts. There is an emphasis on workplace or jobrelated career situations (such as the decisions of a Meteorologist in Section 2.1, a phychologist in Section 7.6, or a Webmaster in Section 9.4) as well as decision making in general (such as choosing a longdistance telephone plan in Section 4.3 or choosing an online service in Section 5.4 or deciding between two job offers in Section 11.1).
Mental Mathematics. These problems are found at the beginning of many exercise sets. They are mental warmups that reinforce concepts found in the accompanying section and increase students' confidence before they tackle an exercise set. By relying on their own mental skills, students increase not only their confidence in themselves but also their number sense and estimation ability.
Writing Exercises. These exercises now found in almost every exercise set are marked with a pencil icon. They require students to assimilate information and provide a written response to explain concepts or justify their thinking. Guidelines recommended by the American Mathematical Association of Two Year Colleges (AMATYC) and other professional groups recommend incorporating writing in mathematics courses to reinforce concepts. Writing opportunities also occur within features such as Spotlight on Decision Making and Chapter Projects.
Data and Graphical Interpretation. Throughout the text there is an emphasis on data interpretation in exercises via tables, bar charts, line graphs, or circle graphs. The ability to interpret data and read and create a variety of graphs is developed gradually so students become comfortable with it.
Review Exercises. These exercises occur in each exercise set (except for those in Chapter 1). These problems are keyed to earlier sections and review concepts learned earlier in the text that are needed in the next section or in the next chapter. These exercises show the links between earlier topics and later material.
A Look Ahead. These exercises occur at the end of some exercise sets. This section contains examples and problems similar to those found in a subsequent algebra course. "A Look Ahead" is presented as a natural extension of the material and contains an example followed by advanced exercises.
In addition to the approximately 5,000 exercises within sections, exercises may also be found in the Vocabulary Checks, Chapter Reviews, Chapter Tests, and Cumulative Reviews.
Vocabulary Checks. Vocabulary checks, new to this edition, provide an opportunity for students to become more familiar with the use of mathematical terms as they strengthen their verbal skills.
Chapter Review and Chapter Test. The end of each chapter contains a review of topics introduced in the chapter. The review problems are keyed to sections. The chapter test is not keyed to sections.
Cumulative Review. Each chapter after the first contains a cumulative review of all chapters beginning with the first up through the chapter at hand. Each problem contained in the cumulative review is actually an earlier worked example in the text that is referenced in the back of the book along with the answer. Students who need to see a complete workedout solution, with explanation, can do so by turning to the appropriate example in the text.
KEY CONTENT FEATURES IN THE SECOND EDITION
Overview. This new edition retains many of the factors that have contributed to its success. Even so, every section of the text was carefully reexamined. Throughout the new edition you will find numerous new applications, examples, and many reallife applications and exercises. For example, look at Sections 2.4, 2.6, or 8.2. Some sections have internal reorganization to better clarify and enhance the presentation.
Increased Integration of Geometry Concepts. In addition to the traditional topics in algebra courses, this text contains a strong emphasis on problem solving, and geometric concepts are integrated throughout. The geometry concepts presented are those most important to a student's understanding of algebra, and I have included many applications and exercises devoted to this topic. These are marked with the geometry icon. Also, geometric figures, a review of angles, lines, and special triangles, are covered in the appendices. The inside back cover provides a quick reference of geometric formulas.
Real Numbers and Algebraic Expressions. Chapter 1 now begins with Tips for Success in Mathematics (Section 1.0). Chapter 1 has been streamlined and refreshed for greater efficiency and relevance. New applications and real data enhance the chapter.
Early and Intuitive Introduction to Graphs and Functions. As bar and line graphs are gradually introduced in Chapter 1, an emphasis is placed on the notion of paired data. This leads naturally to the concepts of ordered pair and the rectangular coordinate system introduced in Chapter 2. This edition offers more real data and conceptual type applications and further strengthens the introduction to slope.
Once students are comfortable with graphing equations, functions are introduced in Chapter 2. The concept of function is illustrated in numerous ways to ensure student understanding: by listing ordered pairs of data, showing rectangular coordinate system graphs, visually representing set correspondences, and including numerous realdata and conceptual examples. The importance of a function is continuously reinforced by not treating it as a single, standalone topic but by constantly integrating functions in appropriate sections of this text.
Increased Attention to Problem Solving. Building on the strengths of the prior edition, a special emphasis and strong commitment are given to contemporary, accessible, and practical applications of algebra. Real data was drawn from a variety of sources including internet sources, magazines, newspapers, government publications, and reference books. Unique Spotlight on Decision Making exercises and a new fourstep problemsolving process are incorporated throughout to focus on helping to build students' problemsolving skills.
Increased Opportunities for Using Technology. Optional explorations for a graphing calculator (or graphing utility such as Texas Instruments Interactive), are integrated appropriately throughout the text in the Discover the Concept feature. The MartinGay/Greene Companion Website includes links to Internet sites to allow opportunities for finding data and using it for problem solving such as with the accompanying online Real World Activities. The Website also includes links to search potential mathematically related careers branching from the chapter openers. Instructors may also choose from a variety of distance learning or online delivery options including Blackboard or Web CT.
Increased Range of Problem Solving. Techniques Access to today's technology lets us expand the range of problems and problemsolving techniques. New ways to learn and solve problems include more attention to graphical and numerical representations.
A special emphasis and strong commitment are given to contemporary and practical applications of algebra. Real data was drawn from a variety of sources including magazines, newspapers, government publications, and reference books. Generating and using personal real data are also encouraged.
Data Interpretation. Data interpretation via tables and graphs begins in the first section of the book and continues throughout the text. The ability to interpret data from tables, screen displays, and a variety of types of graphs including bar, line, and circle graphs is developed gradually so students become comfortable with it.
New Examples. Detailed stepbystep examples were added, deleted, replaced, or updated as needed. Many of these reflect real life. Examples are used in two ways. Often there are numbered, formal examples, and occasionally an example or application is used to introduce a topic or informally discuss the topic. We have included examples that show algebraic, numerical, and/or graphical approaches to solving and checking solutions. See Section 3.1, p.197.
New Exercises. A significant amount of time was spent on the exercise sets. New exercises and examples help address a wide range of student learning styles and abilities. The text now includes the following types of exercises: spotlight on decisionmaking exercises, mental math, computational exercises, reallife applications, writing exercises, muftipart exercises, review exercises, a look ahead exercises, calculator or graphing calculator exercises, data analysis from tables and graphs, vocabulary checks, and projects for individual or group assignment. Also available are new online Real World Activities accessed via this textbook's companion website, and a selection of group activities in a worksheet ready, easytouse format, found in the Instructor's Resource Manual with Tests.
Enhanced Supplements Package. The new Second Edition is supported by a wealth of supplements designed for added effectiveness and efficiency. New items include the MathPro 4.0 Explorer tutorial software together with a unique video clip feature, a new computerized testing system TestGenEQ, and an expanded and improved MartinGay companion website. Some highlights in print materials include the addition of teaching tips in the Annotated Instructor's Edition, and an expanded Instructor's Resource Manual with Tests including additional exercises and short group activities in a readytouseformat. Please see the list of supplements for descriptions.
OPTIONS FOR ONLINE AND DISTANCE LEARNING
For maximum convenience, Prentice Hall offers online interactivity and delivery options for a variety of distance learning needs. Instructors may access or adopt these in conjunction with this text, Intermediate Algebra: A Graphing Approach, Second Edition.
Companion Website
Visit http://www.prenhall.com/martingay
The companion Website includes basic distance learning access to provide links to the text's Real World Activities, careerrelated sites referenced in the chapter opening pages and a selection of online self quizzes. Email is available. For quick reference, the inside front cover of this text also lists the companion Website URL.
WebCT
WebCT includes distance learning access to content found in the MartinGay Companion Website plus more: WebCT provides tools to create, manage, and use online course materials. Save time and take advantage of items such as online help, communication tools, and access to instructor and student manuals. Your college may already have WebCT's software installed on their server or you may choose to download it. Contact your local Prentice Hall sales representative for details.
Blackboard
Visit http://www.prenhall.comldemo
For distance learning access to content and features from the MartinGay Companion Website plus more, Blackboard provides simple templates and tools to create, manage, and use online course materials. Save time and take advantage of items such as online help, course management tools, communication tools, and access to instructor and student manuals. No technical experience required. Contact your local Prentice Hall sales representative for details.
For a complete computerbased internet course
Prentice Hall Interactive Math
Visit http://www.prenhall.com/interactive_math
Prentice Hall Interactive Math is an exciting, proven choice to help students succeed in math. Created for a computerbased course, it provides the effective teaching philosophy of K. Elayn MartinGay in an Internetbased course format. Interactive Math, Intermediate Algebra, takes advantage of stateoftheart technology to provide highly flexible and userfriendly course management tools and an engaging, highly interactive student learning program that easily accommodates the variety of learning styles and broad spectrum of students presented by the typical intermediate algebra class. Personalized learning includes reading, writing, watching video clips, and exploring concepts through interactive questions and activities. Contact your local Prentice Hall sales representative for details.
SUPPLEMENTS FOR THE INSTRUCTOR
Printed Supplements
Annotated Instructor's Edition (ISBN 0130166340)
Instructor's Solutions Manual (ISBN 0130173347)
Instructor's Resource Manual with Tests (ISBN 0130173355)
Media Supplements
TestGen EQ CDROM (Windows/Macintosh) (ISBN 0130890987)
Computerized Tutorial Software Course Management Tools
MathPro 4.0 Explorer Network CDRom (ISBN 013018585X)
Companion Website: http://www.prenhall.com/martingay
SUPPLEMENTS FOR THE STUDENT
Printed Supplements
Student Solutions Manual (ISBN 0130173339)
Student Study Guide (ISBN 0130173371)
How to Study Mathematics
Math on the Internet: A Student's Guide
Media Supplements
Computerized Tutorial Software
MathPro 4.0 Explorer Network CDRom (ISBN 013018585X)
MathPro 4.0 Explorer Student CDRom (ISBN 0130185868)
Videotape Series (ISBN 0130185809)
Companion Website: www.prenhall.com/martingay