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College algebra concepts and contexts9/27/2023 ■ Linear Functions A linear function is a function of the form f 1x2 = b + mx ■ The graph of f is a line with slope m and y-intercept b y y b b x x Ï=b ■ Ï=b+mx Exponential Functions An exponential function is a function of the form f 1x2 = Ca x ■ The graph of f has one of the shapes shown ■ If a 1, then a is called the growth factor and r = a - is called the growth rate ■ If a 1, then a is called the decay factor and r = a - is called the decay rate y y 1 Ï=a˛, a>1 ■ x x Ï=a˛, 00 ■ x y=a(x-h)™+k a>0, h>0, k>0 Power Functions A power function is a function of the form f 1x = Cx p ■ Graphs of some power functions are shown Positive powers y y y x x x x Ï=x£ Ï=≈ y Ï=x¢ Ï=x∞ Fractional powers y y y x x £x Ï=œ ∑ Ï=œ∑ x y x x ∞x Ï= œ∑ ¢x Ï= œ ∑ Negative powers y y y x Ï= x1 y x Ï=≈ x Ï=x£ x Ï= x¢ College Algebra CONCEPTS AND CONTEXTS ABOUT THE AUTHORS 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 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
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