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Functions Modeling Change: A Preparation for Calculus

Functions Modeling Change: A Preparation for Calculus


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About the Book

The fifth edition of Functions Modeling Change: A Preparation for Calculus, 5th Edition helps instructors motivate concepts, and students develop critical thinking skills. Functions Modeling Change, 5th edition, is designed to accomplish the main goals of the Precalculus course: to build a solid mathematical foundation and prepare students for Calculus. The authors achieve this by focusing on a small number of key topics, thereby emphasizing depth of understanding rather than breadth of coverage. Functions Modeling Change, 5th edition, presents each function symbolically, numerically, graphically and verbally (the Rule of Four). Additionally, a large number of real-world applications, examples, and problems enable students to create mathematical models that relate to the world around them.

Table of Contents:
1 Linear Functions and Change 1 1.1 Functions and Function Notation 2 1.2 Rate of Change 10 1.3 Linear Functions 18 1.4 Formulas for Linear Functions 27 1.5 Modeling with Linear Functions 37 1.6 Fitting Linear Functions to Data 46 Review Problems 52 Strengthen Your Understanding 60 Skills Refresher for Chapter One: Linear Equations 62 2 Functions 69 2.1 Input and Output 70 2.2 Domain and Range 78 2.3 Piecewise-Defined Functions 84 2.4 Preview of Transformations: Shifts 90 2.5 Preview of Composite and Inverse Functions 97 2.6 Concavity 104 Review Problems 109 Strengthen Your Understanding 113 3 Quadratic Functions 115 3.1 Introduction to the Family of Quadratic Functions 116 3.2 The Vertex of a Parabola 122 Review Problems 129 Strengthen Your Understanding 130 Skills Refresher for Chapter 3 131 Skills for Factoring 131 Completing the Square 136 4 Exponential Functions 139 4.1 Introduction to the Family of Exponential Functions 140 4.2 Comparing Exponential and Linear Functions 149 4.3 Graphs of Exponential Functions 157 4.4 Applications to Compound Interest 165 4.5 The Number E 168 Review Problems 176 Strengthen Your Understanding 182 Skills Refresher for Chapter 4: Exponents 183 5 Logarithmic Functions 187 5.1 Logarithms and Their Properties 188 5.2 Logarithms and Exponential Models 195 5.3 The Logarithmic Function and Its Applications 203 5.4 Logarithmic Scales 214 Review Problems 225 Strengthen Your Understanding 228 Skills Refresher for Chapter 5: Logarithms 229 6 Transformations of Functions and Their Graphs 233 6.1 Shifts, Reflections, and Symmetry 234 6.2 Vertical Stretches and Compressions 243 6.3 Horizontal Stretches and Combinations of Transformations 250 Review Problems 259 Strengthen Your Understanding 263 7 Trigonometry and Periodic Functions 265 7.1 Introduction to Periodic Functions 266 7.2 The Sine and Cosine Functions 272 7.3 Radians and Arc Length 279 7.4 Graphs of the Sine and Cosine 286 7.5 Sinusoidal Functions 293 7.6 The Tangent Function 301 7.7 Trigonometric Relationships and Identities 304 7.8 Inverse Trigonometric Functions 310 Review Problems 315 Strengthen Your Understanding 319 Skills Refresher for Chapter 7: Special Angles 322 8 Triangle Trigonometry and Polar Coordinates 327 8.1 Trig Functions and Right Triangles 328 8.2 Non-Right Triangles 335 8.3 Polar Coordinates 342 Review Problems 350 Strengthen Your Understanding 352 9 Trigonometric Identities, Models, and Complex Numbers 353 9.1 Trigonometric Equations 354 9.2 Identities, Expressions, and Equations 358 9.3 Sum and Difference Formulas for Sine and Cosine 365 9.4 Trigonometric Models and Sum Identities 369 9.5 Sums with Different Periods and Accoustic Beats 381 9.6 Complex Numbers and De Moivre’s Theorem 385 Review Problems 393 Strengthen Your Understanding 396 10 Compositions, Inverses, and Combinations of Functions 397 10.1 Composition of Functions 398 10.2 Invertibility and Properties of Inverse Functions 404 10.3 Combinations of Functions 414 Review Problems 424 Strengthen Your Understanding 430 11 Polynomial and Rational Functions 431 11.1 Power Functions and Proportionality 432 11.2 Polynomial Functions 443 11.3 The Short-Run Behavior of Polynomials 451 11.4 Rational Functions 457 11.5 The Short-Run Behavior of Rational Functions 464 11.6 Comparing Power, Exponential, and Log Functions 471 11.7 Fitting Exponentials and Polynomials to Data 476 Review Problems 484 Strengthen Your Understanding 489 Skills Refresher for Chapter 11: Algebraic Fractions 491 12 Vectors and Matrices 495 12.1 Vectors 496 12.2 The Components of a Vector 503 12.3 Applications of Vectors 510 12.4 The Dot Product 516 12.5 Matrices 522 Review Problems 531 Strengthen Your Understanding 534 13 Sequences and Series 535 13.1 Sequences 536 13.2 Defining Functions Using Sums: Arithmetic Series 541 13.3 Finite Geometric Series 548 13.4 Infinite Geometric Series 553 Review Problems 559 Strengthen Your Understanding 561 14 Parametric Equations and Conic Sections (Online Only) 14-1 14.1 Parametric Equations 14-2 14.2 Implicitly Defined Curves and Circles 14-11 14.3 Ellipses 14-15 14.4 Hyperbolas 14-18 14.5 Geometric Properties of Conic Sections 14-22 14.6 Hyperbolic Functions 14-36 Review Problems 14-40 Strengthen Your Understanding 14-41 Answers to Odd Problems 563 Index 599

About the Author :
Eric Connally is the director of engineering for the Mathematics Consortium Working Group. He grew up in Texas and moved to Massachusetts after graduating from Cornell University. He has taught math and developed new math curricula at Harvard College, Harvard Extension School, Harvard Kennedy School, and Wellesley College. In 2005, he was given the Petra T. Shattuck Award For Excellence in Teaching. He is a member of a consortium of mathematicians and math educators who have published numerous widely adopted math texts. He has also worked as a software engineer at Elytics, Inc. Deborah Hughes-Hallett is the author of Functions Modeling Change: A Preparation for Calculus, 5th Edition, published by Wiley. Andrew M. Gleason is the author of Functions Modeling Change: A Preparation for Calculus, 5th Edition, published by Wiley.

Review :
“Additionally, a large number of real-world applications, examples, and problems enable students to create mathematical models that relate to the world around them.”  (Zentralblatt MATH, 1 March 2015)


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Product Details
  • ISBN-13: 9781118583197
  • Publisher: John Wiley & Sons Inc
  • Publisher Imprint: John Wiley & Sons Inc
  • Height: 265 mm
  • No of Pages: 640
  • Sub Title: A Preparation for Calculus
  • Width: 216 mm
  • ISBN-10: 1118583191
  • Publisher Date: 04 Aug 2015
  • Binding: Paperback
  • Language: English
  • Spine Width: 24 mm
  • Weight: 1268 gr


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