College Algebra Concepts and Models

by Larson, Ron; Hostetler, Robert P.; Hodgkins, Anne V.

• ISBN13: 9780618492817
• ISBN10: 061849281X
• Edition: 5th
• Format: Hardcover
• Copyright: 2005-01-26
• Publisher: Cengage Learning

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