y x y x Ï=b b Ï=b+mx b ■ Linear Functions A linear function is a function of the form . ■ The graph of f is a line with slope m and y-intercept b. f 1x2 = b + mx ■ Exponential Functions An exponential function is a function of the form . ■ The graph of f has one of the shapes shown. ■ If , then a is called the growth factor and is called the growth rate. ■ If , then a is called the decay factor and is called the decay rate. r = a - 1 a 6 1 r = a - 1 a 7 1 f 1x2 = Cax y y x x 0 1 0 1 Ï=a˛, 0<a<1 Ï=a˛, a>1 ■ Logarithmic Functions A logarithmic function with base is a function of the form . By definition, if and only if ■ The graph of f has the general shape shown below. ■ Basic properties: , , , alogax = x loga ax = x loga a = 1 loga1 = 0 ay = x loga x = y f 1x2 = loga x a 7 1 y 1 x 0 Ï=loga x, a>1 ■ Quadratic Functions A quadratic function is a function of the form . ■ The graph of f has the shape of a parabola. ■ The maximum or minimum value of f occurs at . ■ The function f can be expressed in the standard form . ■ The vertex of the graph of f is at the point (h, k). f 1x2 = a1x - h2 2 + k x = - b 2a f 1x2 = ax2 + bx + c y y x x 0 (h, k) y=a(x-h)™+k a<0, h>0, k>0 y=a(x-h)™+k a>0, h>0, k>0 0 (h, k) ■ Power Functions A power function is a function of the form . ■ Graphs of some power functions are shown. f 1x2 = Cxp Fractional powers y y y y x x x x Ï=≈ Ï=x£ Ï=x¢ Ï=x∞ Ï=œ∑x Ï=£œ∑x Ï= ¢œ∑x Ï= ∞œ∑x y x y x y x y x Positive powers Negative powers Ï= Ï= Ï= Ï= x 1 ≈ 1 x£ 1 x¢ 1 y x y x y x y x College Algebra CONCEPTS AND CONTEXTS JAMES STEWART received his MS from Stanford University and his PhD from the University of Toronto. He did research at the University of London and was influenced by the famous mathematician George Polya at Stanford University. Stewart is Professor Emeritus at McMaster University and is currently Professor of Mathematics at the University of Toronto. His research field is harmonic analysis and the connections between mathematics and music. James Stewart is the author of a bestselling calculus textbook series published by Brooks/Cole, Cengage Learning, including Calculus, Calculus: Early Transcendentals, and Calculus: Concepts and Contexts; a series of precalculus texts; and a series of high-school mathematics textbooks. LOTHAR REDLIN grew up on Vancouver Island, received a Bachelor of Science degree from the University of Victoria, and received a PhD from McMaster University in 1978. He subsequently did research and taught at the University of Washington, the University of Waterloo, and California State University, Long Beach. He is currently Professor of Mathematics at The Pennsylvania State University, Abington Campus. His research field is topology. SALEEM WATSON received his Bachelor of Science degree from Andrews University in Michigan. He did graduate studies at Dalhousie University and McMaster University, where he received his PhD in 1978. He subsequently did research at the Mathematics Institute of the University of Warsaw in Poland. He also taught at The Pennsylvania State University. He is currently Professor of Mathematics at California State University, Long Beach. His research field is functional analysis. PHYLLIS PANMAN received a Bachelor of Music degree in violin performance in 1987 and a PhD in mathematics in 1996 from the University of Missouri at Columbia. Her research area is harmonic analysis. As a graduate student she taught college algebra and calculus courses at the University of Missouri. She continues to teach and tutor students in mathematics at all levels, including conducting mathematics enrichment courses for middle school students. Stewart, Redlin, and Watson have also published Precalculus: Mathematics for Calculus, Algebra and Trigonometry, and Trigonometry. ABOUT THE AUTHORS About the Cover Each of the images on the cover appears somewhere within the pages of the book itself—in real-world examples, exercises, or explorations. The many and varied applications of algebra that we study in this book highlight the importance of algebra in understanding the world around us, and many of these applications take us to places where we never thought mathematics would go. The global montage on the cover is intended to echo this universal reach of the applications of algebra. College Algebra CONCEPTS AND CONTEXTS James Stewart McMaster University and University of Toronto Lothar Redlin The Pennsylvania State University Saleem Watson California State University, Long Beach Phyllis Panman Australia • Brazil • Japan • Korea • Mexico • Singapore • Spain • United Kingdom • United States College Algebra: Concepts and Contexts James Stewart, Lothar Redlin, Saleem Watson, Phyllis Panman Acquisitions Editor: Gary Whalen Developmental Editor: Stacy Green Assistant Editor: Cynthia Ashton Editorial Assistant: Guanglei Zhang Media Editor: Lynh Pham Marketing Manager: Myriah Fitzgibbon Marketing Assistant: Angela Kim Marketing Communications Manager: Katy Malatesta Content Project Manager: Jennifer Risden Creative Director: Rob Hugel Art Director: Vernon Boes Print Buyer: Judy Inouye Rights Acquisitions Account Manager, Text: Roberta Broyer Rights Acquisitions Account Manager, Image: Don Schlotman Production Service: Martha Emry Text Designer: Lisa Henry Art Editor: Martha Emry Photo Researcher: Bill Smith Group Copy Editor: Barbara Willette Illustrator: Jade Myers, Matrix Art Services; Network Graphics Cover Designer: Larry Didona Cover Images: giant trees (Cate Frost/Shutterstock.com 2009); black-browed albatross (Armin Rose/ Shutterstock .com 2009); church (Vladislav Gurfinkel/Shutterstock .com 2009); student in chemistry lab (Laurence Gough/Shutterstock 2009); five skydivers performing formations (Joggie Botma/Shutterstock.com 2009); Shanghai at sunset (David Roos/Shutterstock.com 2009); combine harvester working on wheat crop (Stephen Mcsweeny/Shutterstock.com 2009); howler monkeys (Christopher Marin/ Shutterstock. com 2009); family making sand castle (Magdalena Bujak/ Shutterstock.com 2009); Easter Island (Vladimir Korostyshevskiy/ Shutterstock.com 2009); giardia (Sebastian Kaulitzki/Shutterstock.com 2009); female in handcuffs (Jack Dagley Photography/Shutterstock.com 2009); red eye tree frog (Luis Louro/Shutterstock.com 2009); humpback whale (Josef78/Shutterstock.com 2009); businessman in car (Vladimir Mucibabic/Shutterstock.com 2009); origami birds (Slash331/Shutterstock.com 2009); pine forest (James Thew/Shutterstock.com 2009); house finch (Steve Byland/Shutterstock.com 2009); mother with baby (Lev Dolgachov/Shutterstock.com 2009); bacteria (Tischenko Irina/Shutterstock.com 2009); Dos Amigos pumping plant (Aaron Kohr/Shutterstock.com 2009); polar bears (Keith Levit/Shutterstock.com 2009); combine harvester (Orientaly/Shutterstock.com 2009); streptococcus (Sebastian Kaulitzki/Shutterstock.com 2009); jumping girl (Studio1One/Shutterstock.com 2009); traffic (Manfred Steinbach/Shutterstock.com 2009); hybrid car (Jonathan Larsen/Shutterstock.com 2009); woman driving car (Kristian Sekulic/Shutterstock .com 2009); woman hiding money under mattress (cbarnesphotography/Shutterstock.com 2009); Mount Kilimanjaro (Peter Zaharov/Shutterstock.com 2009) Compositor: S4Carlisle Publishing Services © 2011 Brooks/Cole, Cengage Learning ALL RIGHTS RESERVED. 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