Tecnico

College Algebra
Version π = 3 by

Carl Stitz, Ph.D. Jeff Zeager, Ph.D. Lakeland Community College Lorain County Community College Cover Design Dario Rampersad Photo Credits Jessica S. Novak, Lakeland Community College Ron Jantz, Lorain County Community College Lauren Potter, WebAssign July 15, 2011

ii Acknowledgements While the cover of this textbook lists only two names, the book as itstands today would simply not exist if not for the tireless work and dedication of several people. First and foremost, we wish to thank our families for their patience and support during the creative process. We would also like to thank our students - the sole inspiration for the work. Among our colleagues, we wish to thank Rich Basich, Bill Previts, and Irina Lomonosov, who not only were earlyadopters of the textbook, but also contributed materials to the project. Special thanks go to Katie Cimperman, Terry Dykstra, Frank LeMay, and Rich Hagen who provided valuable feedback from the classroom. Thanks also to David Stumpf, Ivana Gorgievska, Jorge Gerszonowicz, Kathryn Arocho, Heather Bubnick, and Florin Muscutariu for their unwaivering support (and sometimes defense!) of the project. Fromoutside the classroom, we wish to thank Don Anthan and Ken White, who designed the electric circuit applications used in the text, as well as Drs. Wendy Marley and Marcia Ballinger for the Lorain CCC enrollment data used in the text. The authors are also indebted to the good folks at our schools’ bookstores, Gwen Sevtis (Lakeland CC) and Chris Callahan (Lorain CCC), for working with us to getprinted copies to the students as inexpensively as possible. We would also like to thank Lakeland folks Jeri Dickinson, Mary Ann Blakeley, Jessica Novak, and Corrie Bergeron for their enthusiasm and promotion of the project. The administration at both schools have also been very supportive of the project, so from Lakeland, we wish to thank Dr. Morris W. Beverage, Jr., President, Dr. Fred Law, Provost,Deans Don Anthan and Dr. Steve Oluic, and the Board of Trustees. From Lorain County Community College, we which to thank Dr. Roy A. Church, Dr. Karen Wells, and the Board of Trustees. From the Ohio Board of Regents, we wish to thank former Chancellor Eric Fingerhut, Darlene McCoy, Associate Vice Chancellor of Affordability and Efficiency, and Kelly Bernard. From OhioLINK, we wish to thank SteveAcker, John Magill, and Stacy Brannan. We also wish to thank the good folks at WebAssign, most notably Chris Hall, COO, and Joel Hollenbeck (former VP of Sales.) Last, but certainly not least, we wish to thank all the folks who have contacted us over the interwebs, most notably Dimitri Moonen and Joel Wordsworth, who gave us great feedback, and Antonio Olivares who helped debug the source code.Table of Contents
Preface 1 Relations and Functions 1.1 Sets of Real Numbers and The Cartesian 1.1.1 Sets of Numbers . . . . . . . . . 1.1.2 The Cartesian Coordinate Plane 1.1.3 Distance in the Plane . . . . . . 1.1.4 Exercises . . . . . . . . . . . . . 1.1.5 Answers . . . . . . . . . . . . . . 1.2 Relations . . . . . . . . . . . . . . . . . 1.2.1 Graphs of Equations . . . . . . . 1.2.2 Exercises .. . . . . . . . . . . . 1.2.3 Answers . . . . . . . . . . . . . . 1.3 Introduction to Functions . . . . . . . . 1.3.1 Exercises . . . . . . . . . . . . . 1.3.2 Answers . . . . . . . . . . . . . . 1.4 Function Notation . . . . . . . . . . . . 1.4.1 Modeling with Functions . . . . 1.4.2 Exercises . . . . . . . . . . . . . 1.4.3 Answers . . . . . . . . . . . . . . 1.5 Function Arithmetic . . . . . .. . . . . 1.5.1 Exercises . . . . . . . . . . . . . 1.5.2 Answers . . . . . . . . . . . . . . 1.6 Graphs of Functions . . . . . . . . . . . 1.6.1 General Function Behavior . . . 1.6.2 Exercises . . . . . . . . . . . . . 1.6.3 Answers . . . . . . . . . . . . . . 1.7 Transformations . . . . . . . . . . . . . . 1.7.1 Exercises . . . . . . . . . . . . . 1.7.2 Answers . . . . . . . . . . . . . . ix 1...