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College Algebra

Concepts Through Functions


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College Algebra: Concepts Through Functions by Michael Sullivan
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This new text embodies Sullivan/Sullivan's hallmarks - accuracy, precision, depth, strong student support, and abundant exercises while exposing students early (Chapter One) to the study of functions. "IT WORKS" for instructors and students because it focuses students on the fundamentals: "preparing "for class, "practicing "their homework, and "reviewing," After completing the book, students will be prepared to handle the algebra found in subsequent courses such as finite mathematics, business mathematics, and engineering calculus and will have a solid understanding of the concept of a function.

Table of Contents

FOUNDATIONS: A PRELUDE TO FUNCTIONS F.1 The Distance and Midpoint Formulas F.2 Graphs of Equations; Intercepts; Symmetry F.3 Lines F.4 Circles Chapter 1 Functions and Their Graphs 1.1 Functions 1.2 The Graph of a Function 1.3 Properties of Functions 1.4 Library of Functions; Piecewise-defined Functions 1.5 Graphing Techniques: Transformations 1.6 Mathematical Models: Constructing Functions Chapter Review Chapter Test Chapter Projects Chapter 2 Linear and Quadratic Functions 2.1 Properties of Linear Functions 2.2 Building Linear Functions from Data; Direct Variation 2.3 Quadratic Functions and Their Real Zeros 2.4 Properties of Quadratic Functions 2.5 Inequalities Involving Quadratic Functions 2.6 Quadratic Models; Building Quadratic Functions From Data 2.7 Complex Zeros of a Quadratic Function 2.8 Equations and Inequalities Involving the Absolute Value Function Chapter Review Chapter Test Chapter Projects Cumulative Review Chapter 3 Polynomial and Rational Functions 3.1 Polynomial Functions and Models 3.2 Properties of Rational Functions 3.3 The Graph of a Rational Function; Inverse and Joint Variation 3.4 Polynomial and Rational Inequalities 3.5 The Real Zeros of a Polynomial Function 3.6 Complex Zeros: Fundamental Theorem of Algebra Chapter Review Chapter Test Chapter Project Cumulative Review Chapter 4 Exponential and Logarithmic Functions 4.1 Composite Functions 4.2 One-to-One Functions; Inverse Functions 4.3 Exponential Functions 4.4 Logarithmic Functions 4.5 Properties of Logarithms 4.6 Logarithmic and Exponential Equations 4.7 Compound Interest 4.8 Exponential Growth and Decay; Newton's Law; Logistic Growth and Decay 4.9 Building Exponential, Logarithmic, and Logistic Functions from Data Chapter Review Chapter Test Chapter Project Cumulative Review Chapter 5 Analytic Geometry 5.1 Conics 5.2 The Parabola 5.3 The Ellipse 5.4 The Hyperbola Chapter Review Chapter Test Chapter Projects Cumulative Review Chapter 6 Systems of Equations and Inequalities 6.1 Systems of Linear Equations: Substitution and Elimination 6.2 Systems of Linear Equations: Matrices 6.3 Systems of Linear Equations: Determinants 6.4 Matrix Algebra 6.5 Partial Fraction Decomposition 6.6 Systems of Nonlinear Equations 6.7 Systems of Inequalities 6.8 Linear Programming Chapter Review Chapter Test Chapter Projects Cumulative Review Chapter 7 Sequences; Induction; The Binomial Theorem 7.1 Sequences 7.2 Arithmetic Sequences 7.3 Geometric Sequences; Geometric Series 7.4 Mathematical Induction 7.5 The Binomial Theorem Chapter Review Chapter Test Chapter Projects Cumulative Review Chapter 8 Counting and Probability 8.1 Sets and Counting 8.2 Permutations and Combinations 8.3 Probability Chapter Review Chapter Test Chapter Project Cumulative Review Appendix A Review A.1 Algebra Essentials A.2 Geometry Essentials A.3 Polynomials A.4 Factoring Polynomials A.5 Synthetic Division A.6 Rational Expressions A.7 nth Roots; Rational Exponents A.8 Solving Equations Algebraically A.9 Interval Notation; Solving Inequalities A.10 Problem Solving: Applications of Linear Equations A.11 Complex Numbers Appendix B Graphing Utilities B.1 The Viewing Rectangle B.2 Graphing Equations in Two Variables B.3 Locating Intercepts and Checking for Symmetry B.4 Solving Equations Using a Graphing Utility B.5 Square Screens B.6 Graphing Inequalities in Two Variables B.7 Solving Systems of Linear Equations Answers Index

Author Biography

Mike Sullivan Professor of Mathematics at Chicago State University received a Ph.D. in mathematics from Illinois Institute of Technology. Mike has taught at Chicago State for over 30 years. He is a native of Chicago's South Side and currently resides in Oaklawn. Mike has four children. The two oldest have degrees in mathematics and assisted in proofing, checking examples and exercises, and writing solutions manuals for this project. Mike III co-authored the Sullivan Graphing with Data Analysis series as well as this series. Dan, the youngest, sells for Prentice Hall as a generalist. Mike has authored or co-authored over ten books. He owns a travel agency, and splits his time between a condo in Naples, Florida and a home in Oaklawn, where Mike enjoys gardening. Mike first signed this series with Deleen Publishing (Acquired by Macmillan) in 1985. Mike Sullivan III is a professor of mathematics at Joliet Junior College. He holds graduate degrees from Depot University in both mathematics and economics. Mike has co-authored both of the Sullivan graphing series and collaborated with his sister to author supplements for all of the Sullivan series. Mike has recently authored a brand new successful Statistics book for Prentice Hall Fundamentals of Statistics, 1/e 2005 and Statistics: Informed Decisions Using Data, 1/e, 2004. Mike is currently working on a developmental math series for Prentice Hall that will be published in 2007. Mike is the father of three children. He is an avid golfer and tries to spend as much of his limited free time as possible on the golf course. Why We Wrote the Book: Work on this series began with a unique perspective. Teaching at a large urban institution and a smaller two-year college has allowed us to see firsthand the challenges associated with teaching students with diverse backgrounds in an urban setting. Successful textbooks must be accessible to students. As lead author of this series, one of the most important things I bring to the project is my experience as author of a successful calculus text. Mike and I are both aware that students must be prepared in a Precalculus course for subsequent mathematics courses. We also realize that many College Algebra students will not be going on to take upper level math courses. In this series we resolved the seeming dilemma without sacrificing accessibility. The books in this series are designed to be mathematically comprehensive and to provide substantial mathematical preparation for subsequent courses. At the same time, great effort has been expended to motivate the material and to make it accessible to even poorly prepared students.
Release date NZ
June 1st, 2006
Country of Publication
United States
4th Revised edition
Illustrations (chiefly col.), ports.
Prentice Hall
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