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College Algebra By Carl Stitz, Ph.D.Jeff Zeager, Ph.D. Lakeland Community College Lorain County Community College (All Chapters)

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College Algebra By Carl Stitz, Ph.D.Jeff Zeager, Ph.D. Lakeland Community College Lorain County Community College (All Chapters) 2024/2025 Acknowledgements The authors are indebted to the many people who support this project. From Lakeland Community College, we wish to thank the following p...

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  • June 9, 2024
  • 659
  • 2023/2024
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  • college algebra by carl stitz phdjeff zeager
  • phd lakeland community college lorain county
  • lorain county community college all chapters

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College Algebra By Carl Stitz, Ph.D. Jeff Zeager, Ph.D. Lakeland Community Colleg e Lorain County Community College (All Chapters) 2024/2025 Acknowledgements The authors are indebted to the many people who support this project. From Lakeland Community College, we wish to thank the following people: Bill Previts, who not only class tested the book but added an extraordinary amount of exercises to it; Rich Basich and Ivana Gorgievska, who class tested and promoted the book; Don Anthan and Ken White, who designed the electric circuit applications used in the text; Gwen Sevits, Assistant Bookstore Manager, for her patience and her efforts to get the book to the stud ents in an efficient and economical fashion; Jessica Novak, Marketing and Communication Specialist, for her efforts to promote the book; Corrie Bergeron, Instructional Designer, for his enthusiasm and support of the text and accompanying YouTube videos; Dr . Fred Law, Provost, and the Board of Trustees of Lakeland Community College for their strong support and deep commitment to the project. From Lorain County Community College, we wish to thank: Irina Lomonosov for class testing the book and generating acco mpanying PowerPoint slides; Jorge Gerszonowicz, Kathryn Arocho, Heather Bubnick, and Florin Muscutariu for their unwaivering support of the project; Drs. Wendy Marley and Marcia Ballinger, Lorain CCC, for the Lorain CCC enrollment data used in the text. We would also like to extend a special thanks to Chancellor Eric Fingerhut and the Ohio Board of Regents for their support and promotion of the project. Last, but certainly not least, we wish to thank Dimitri Moonen, our dear friend from across the Atlantic, who took the time each week to e -mail us typos and other corrections. ii Table of Contents Preface ix 1 Relations and Functions 1 1.1 The Cartesian Coordinate Plane . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.1.1 Distance in the Plane . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.1.2 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 1.1.3 Answers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 1.2 Relations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 1.2.1 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 1.2.2 Answers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 1.3 Graphs of Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 1.3.1 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 1.3.2 Answers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 1.4 Introduction to Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 1.4.1 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 1.4.2 Answers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 1.5 Function Notation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 1.5.1 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50 1.5.2 Answers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 1.6 Function Arithmetic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 1.6.1 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60 1.6.2 Answers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62 1.7 Graphs of Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64 1.7.1 General Function Behavior . . . . . . . . . . . . . . . . . . . . . . . . . . . 70 1.7.2 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77 1.7.3 Answers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81 1.8 Transformations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84 1.8.1 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104 1.8.2 Answers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107 Table of Contents 2 Linear and Quadratic Functions 111 2.1 Linear Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111 2.1.1 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123 2.1.2 Answers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126 2.2 Absolute Value Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127 2.2.1 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135 2.2.2 Answers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136 2.3 Quadratic Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139 2.3.1 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148 2.3.2 Answers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150 2.4 Inequalities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154 2.4.1 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167 2.4.2 Answers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 168 2.5 Regression . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 170 2.5.1 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175 2.5.2 Answers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 178 3 Polynomial Functions 179 3.1 Graphs of Polynomials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179 3.1.1 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 190 3.1.2 Answers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193 3.2 The Factor Theorem and The Remainder Theorem . . . . . . . . . . . . . . . . . . 197 3.2.1 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 205 3.2.2 Answers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 206 3.3 Real Zeros of Polynomials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 207 3.3.1 For Those Wishing to use a Graphing Calculator . . . . . . . . . . . . . . . 208 3.3.2 For Those Wishing NOT to use a Graphing Calculator . . . . . . . . . . . 211 3.3.3 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 217 3.3.4 Answers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 218 3.4 Complex Zeros and the Fundamental Theorem of Algebra . . . . . . . . . . . . . . 219 3.4.1 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 227 3.4.2 Answers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 228 4 Rational Functions 231 4.1 Introduction to Rational Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . 231 4.1.1 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 242 4.1.2 Answers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 244 4.2 Graphs of Rational Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 246 4.2.1 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 259 4.2.2 Answers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 261 4.3 Rational Inequalities and Applications . . . . . . . . . . . . . . . . . . . . . . . . . 267 4.3.1 Variation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 272 4.3.2 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 276 Table of Contents v 4.3.3 Answers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 278 iv 5 Further Topics in Functions 279 5.1 Function Composition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 279 5.1.1 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 289 5.1.2 Answers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 291 5.2 Inverse Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 293 5.2.1 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 309 5.2.2 Answers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 310 5.3 Other Algebraic Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 311 5.3.1 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 321 5.3.2 Answers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 324 6 Exponential and Logarithmic Functions 329 6.1 Introduction to Exponential and Logarithmic Functions . . . . . . . . . . . . . . . 329 6.1.1 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 342 6.1.2 Answers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 345 6.2 Properties of Logarithms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 347 6.2.1 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 355 6.2.2 Answers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 357 6.3 Exponential Equations and Inequalities . . . . . . . . . . . . . . . . . . . . . . . . . 358 6.3.1 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 366 6.3.2 Answers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 367 6.4 Logarithmic Equations and Inequalities . . . . . . . . . . . . . . . . . . . . . . . . 368 6.4.1 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 375 6.4.2 Answers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 377 6.5 Applications of Exponential and Logarithmic Functions . . . . . . . . . . . . . . . 378 6.5.1 Applications of Exponential Functions . . . . . . . . . . . . . . . . . . . . . 378 6.5.2 Applications of Logarithms . . . . . . . . . . . . . . . . . . . . . . . . . . . 386 6.5.3 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 391 6.5.4 Answers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 395 7 Hooked on Conics 397 7.1 Introduction to Conics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 397 7.2 Circles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 400 7.2.1 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 404 7.2.2 Answers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 405 7.3 Parabolas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 407 7.3.1 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 415 7.3.2 Answers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 416 7.4 Ellipses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 419 7.4.1 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 428 7.4.2 Answers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 430

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