9780618492817

College Algebra Concepts and Models

by ; ;
  • ISBN13:

    9780618492817

  • ISBN10:

    061849281X

  • Edition: 5th
  • Format: Hardcover
  • Copyright: 1/26/2005
  • Publisher: Cengage Learning

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Summary

College Algebra: Concepts and Modelsprovides a solid understanding of algebra, using modeling techniques and real-world data applications. The text is effective for students who will continue on in mathematics, as well as for those who will end their mathematics education with college algebra. Instructors may also take advantage of optional discovery and exploration activities that use technology and are integrated throughout the text. The Fifth Edition enhances problem solving coverage throughMake a Decisionfeatures. These features are threaded throughout each chapter, beginning with the Chapter Opener application, followed by examples and exercises, and ending with the end-of-chapter project. This edition also features Eduspace, Houghton Mifflin's online learning tool, which allows instructors to teach all or part of a course online, and provides students with additional practice, review, and homework problems. A brief version of this text,College Algebra: A Concise Course,provides a shorter version of the text without the introductory review. New!Make a Decisionfeatures thread through each chapter beginning with the Chapter Opener application, followed by examples and exercises, and ending with the end-of-chapter project. Students are asked to choose which answer fits within the context of a problem, to interpret answers in the context of a problem, to choose an appropriate model for a data set, or to decide whether a current model will continue to be accurate in future years. The student must examine all data and decide upon a final answer. Chapter Projectsextend applications designed to enhance students understanding of mathematical concepts. Real data is previewed at the beginning of the chapter and then analyzed in detail in the Project at the end of the chapter. Here the student is guided through a set of multi-part exercises using modeling, graphing, and critical thinking skills to analyze the data. A variety of exercise typesare included in each exercise set. Questions involving skills, modeling, 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!"In the News"Articles from current media sources (magazines, newspapers, web sites, etc.) have been added to every chapter. Students answer questions that connect the article and the algebra learned in that section. This feature allows students to see the relevancy of what they are learning, and the importance of everyday mathematics. Discussing the Conceptactivities end most sections and encourage students to think, reason, and write about algebra. These exercises help synthesize the concepts and methods presented in the section. Instructors can use these problems for individual student work, for collaborative work or for class discussion. In many sections, problems in the exercise sets have been marked with a special icon in the instructor's edition as alternative discussion/collaborative problem. Discoveryactivities provide opportunities for the exploration of selected mathematical concepts. Students are encouraged to use techniques such as visualization and modeling to develop their intuitive understanding of theoretical concepts. These optional activities can be omitted at the instructor's discretion without affecting the flow of the material. New!EduspaceHoughton Mifflin's online learning tool powered by Blackboard, is a customizable, powerful and interactive platform that provides instructors with text-specific online courses and content.

Table of Contents

A Word from the Authors (Preface) vii
Highlights of Features x
Fundamental Concepts of Algebra
Real Numbers: Order and Absolute Value
2(8)
The Basic Rules of Algebra
10(10)
Integer Exponents
20(9)
Radicals and Rational Exponents
29(11)
Mid-Chapter Quiz
39(1)
Polynomials and Special Products
40(8)
Factoring
48(7)
Fractional Expressions
55(15)
Make a Decision Project: Musical Notes and Frequencies
62(1)
Summary
63(1)
Review Exercises
64(3)
Chapter Test
67(3)
Equations and Inequalities
Linear Equations
70(9)
Mathematical Modeling
79(14)
Quadratic Equations
93(11)
The Quadratic Formula
104(11)
Mid-Chapter Quiz
114(1)
Other Types of Equations
115(11)
Linear Inequalities
126(12)
Other Types of Inequalities
138
Make a Decision Project: Salaries in Professional Baseball
148(1)
Summary
149(1)
Review Exercises
150(4)
Chapter Test
154(1)
Cumulative Test: Chapters R1--R2
155
Functions and Graphs
Graphs of Equations
2(14)
Lines in the Plane
16(12)
Linear Modeling and Direct Variation
28(12)
Functions
40(14)
Mid-Chapter Quiz
53(1)
Graphs of Functions
54(11)
Transformations of Functions
65(9)
The Algebra of Functions
74(10)
Inverse Functions
84(20)
Make a Decision Project: Demographics
94(1)
Summary
95(1)
Review Exercises
96(5)
Chapter Test
101(3)
Polynomial and Rational Functions
Quadratic Functions and Models
104(12)
Polynomial Functions of Higher Degree
116(10)
Polynomial Division
126(10)
Real Zeros of Polynomial Functions
136(15)
Mid-Chapter Quiz
150(1)
Complex Numbers
151(10)
The Fundamental Theorem of Algebra
161(8)
Rational Functions
169(21)
Make a Decision Project: Renewable Energy
181(1)
Summary
182(1)
Review Exercises
183(4)
Chapter Test
187(3)
Exponential and Logarithmic Functions
Exponential Functions
190(12)
Logarithmic Functions
202(10)
Properties of Logarithms
212(9)
Mid-Chapter Quiz
220(1)
Solving Exponential and Logarithmic Equations
221(10)
Exponential and Logarithmic Models
231(23)
Make a Decision Project: Newton's Law of Cooling
244(1)
Summary
245(1)
Review Exercises
246(4)
Chapter Test
250(1)
Cumulative Test: Chapters 1--3
251(3)
Systems of Equations and Inequalities
Solving Systems Using Substitution
254(10)
Solving Systems Using Elimination
264(12)
Linear Systems in Three or More Variables
276(14)
Mid-Chapter Quiz
289(1)
Systems of Inequalities
290(10)
Linear Programming
300(20)
Make a Decision Project: Newspapers
310(1)
Summary
311(1)
Review Exercises
312(5)
Chapter Test
317(3)
Matrices and Determinants
Matrices and Linear Systems
320(14)
Operations with Matrices
334(15)
The Inverse of a Square Matrix
349(11)
Mid-Chapter Quiz
359(1)
The Determinant of a Square Matrix
360(10)
Applications of Matrices and Determinants
370(18)
Make a Decision Project: Market Share
379(1)
Summary
380(1)
Review Exercises
381(4)
Chapter Test
385(3)
Sequences, Series, and Probability
Sequences and Summation Notation
388(10)
Arithmetic Sequences and Partial Sums
398(9)
Geometric Sequences and Series
407(10)
The Binomial Theorem
417(8)
Mid-Chapter Quiz
424(1)
Counting Principles
425(10)
Probability
435(12)
Mathematical Induction
447
Make a Decision Project: The Multiplier Effect
458(1)
Summary
459(1)
Review Exercises
460(4)
Chapter Test
464(1)
Cumulative Test: Chapters 4--6
465
APPENDICES
Appendix A An Introduction to Graphing Utilities
1(7)
Appendix B Conic Sections
Conic Sections
8(12)
Conic Sections and Translations
20(9)
Appendix C Further Concepts in Statistics (available on the web/CD only)
Data and Linear Modeling
Measures of Central Tendency and Dispersion
Answers to Warm Ups, Odd-Numbered Exercises, Quizzes, and Tests 29(70)
Index of Applications 99(5)
Index 104

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