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College Algebra senior contributing author Jay abramson, arizona state University About Our Team Senior Contributing Author Jay Abramson has been teaching College Algebra for 33 years, the last 14 at Arizona State University, where he is a principal lecturer in the School of Mathematics and Statistics. His accomplishments at ASU include co-developing the university’s first hybrid and online math courses as well as an extensive library of video lectures and tutorials. In addition, he has served as a contributing author for two of Pearson Education’s math programs, NovaNet Precalculus and Trigonometry. Prior to coming to ASU, Jay taught at Texas State Technical College and Amarillo College. He received Teacher of the Year awards at both institutions. Contributing Authors Reviewers Valeree Falduto, Palm Beach State College Phil Clark, Scottsdale Community College Rachael Gross, Towson University Michael Cohen, Hofstra University David Lippman, Pierce College Matthew Goodell, SUNY Ulster Melonie Rasmussen, Pierce College Lance Hemlow, Raritan Valley Community College Rick Norwood, East Tennessee State University Dongrin Kim, Arizona State University Nicholas Belloit, Florida State College Jacksonville Cynthia Landrigan, Erie Community College Jean-Marie Magnier, Springfield Technical Community College Wendy Lightheart, Lane Community College Harold Whipple Carl Penziul, Tompkins-Cortland Community College Christina Fernandez Sandra Nite, Texas A&M University Eugenia Peterson, Richard J. Daley College Rhonda Porter, Albany State University The following faculty contributed to the development of OpenStax Michael Price, University of Oregon Precalculus, the text from which this product was updated and derived. 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OpenStax.org Brief Contents 1 Prerequisites 1 2 Equations and Inequalities 73 3 Functions 159 4 Linear Functions 279 5 Polynomial and Rational Functions 343 6 Exponential and Logarithmic Functions 463 7 Systems of Equations and Inequalities 575 8 Analytic Geometry 681 9 Sequences, Probability and Counting Theory 755 v Contents Preface xi 1 Prerequisites 1 1.1 Real Numbers: Algebra Essentials 2 1.2 Exponents and Scientific Notation 17 1.3 Radicals and Rational Expressions 31 1.4 Polynomials 41 1.5 Factoring Polynomials 49 1.6 Rational Expressions 58 Chapter 1 Review 66 Chapter 1 Review Exercises 70 Chapter 1 Practice Test 72 2 Equations and Inequalities 73 2.1 The Rectangular Coordinate Systems and Graphs 74 2.2 Linear Equations in One Variable 87 2.3 Models and Applications 102 2.4 Complex Numbers 111 2.5 Quadratic Equations 119 2.6 Other Types of Equations 131 2.7 Linear Inequalities and Absolute Value Inequalities 142 Chapter 2 Review 151 Chapter 2 Review Exercises 155 Chapter 2 Practice Test 158 3 Functions 159 3.1 Functions and Function Notation 160 3.2 Domain and Range 180 3.3 Rates of Change and Behavior of Graphs 196 3.4 Composition of Functions 209 3.5 Transformation of Functions 222 3.6 Absolute Value Functions 247 3.7 Inverse Functions 254 Chapter 3 Review 267 Chapter 3 Review Exercises 272 Chapter 3 Practice Test 277 vii 4 Linear Functions 279 4.1 Linear Functions 280 4.2 Modeling with Linear Functions 309 4.3 Fitting Linear Models to Data 322 Chapter 4 Review 334 Chapter 4 Review Exercises 336 Chapter 4 Practice Test 340 5 Polynomial and Rational Functions 343 5.1 Quadratic Functions 344 5.2 Power Functions and Polynomial Functions 360 5.3 Graphs of Polynomial Functions 375 5.4 Dividing Polynomials 393 5.5 Zeros of Polynomial Functions 402 5.6 Rational Functions 414 5.7 Inverses and Radical Functions 435 5.8 Modeling Using Variation 446 Chapter 5 Review 453 Chapter 5 Review Exercises 458 Chapter 5 Practice Test 461 6 Exponential and Logarithmic Functions 463 6.1 Exponential Functions 464 6.2 Graphs of Exponential Functions 479 6.3 Logarithmic Functions 491 6.4 Graphs of Logarithmic Functions 499 6.5 Logarithmic Properties 516 6.6 Exponential and Logarithmic Equations 526 6.7 Exponential and Logarithmic Models 537 6.8 Fitting Exponential Models to Data 552 Chapter 6 Review 565 Chapter 6 Review Exercises 570 Chapter 6 Practice Test 573 viii