Functions Modeling Change: A Preparation for Calculus, 2nd Edition

by Eric Connally (Harvard Univ. Extension); Deborah Hughes-Hallett (Univ. of Arizona); Andrew M. Gleason (Harvard Univ.); Philip Cheifetz (Nassau Community College); Daniel E. Flath (Macalester College ); Patti Frazer Lock (St. Lawrence Univ.); Karen Rh

• ISBN13: 9780471266198
• ISBN10: 0471266191
• Edition: 2
• Format: Hardcover
• Copyright: 2003-04-01
• Publisher: Wiley

Summary

This is a new edition of the precalculus text developed by the Consortium based at Harvard University and funded by a National Science Foundation Grant. The text is thought-provoking for well-prepared students while still accessible to students with weaker backgrounds. It provides numerical and graphical approaches as well as algebraic approaches to give students another way of mastering the material. This approach encourages students to persist, thereby lowering failure rates. A large number of real-world examples and problems enable students to create mathematical models that will help them understand the world in which they live. The focus is on those topics that are essential to the study of calculus and these topics are treated in depth. Linear, exponential, power, and periodic functions are introduced before polynomial and rational functions to take advantage of their use to model physical phenomena. Building on the Consortium's Rule of Four: Each function is represented symbolically, numerically, graphically, and verbally where appropriate.

Table of Contents

Functions, Lines, and Change	1	(59)
Functions and Function Notation	2	(8)
Rate of Change	10	(6)
Linear Functions	16	(9)
Formulas for Linear Functions	25	(8)
Geometric Properties of Linear Functions	33	(9)
Fitting Linear Functions to Data	42	(17)
Review Problems	48	(4)
Check Your Understanding	52	(2)
Tools for Chapter One: Linear Equations	54	(5)
Functions, Quadratics, and Concavity	59	(42)
Input and Output	60	(6)
Domain and Range	66	(5)
Piecewise Defined Functions	71	(6)
Inverse Functions	77	(3)
Concavity	80	(5)
Quadratic Functions	85	(16)
Review Problems	90	(3)
Check Your Understanding	93	(1)
Tools for Chapter 2: Quadratic Equations	94	(7)
Exponential Functions	101	(42)
Introduction to the Family of Exponential Functions	102	(8)
Comparing Exponential and Linear Functions	110	(8)
Graphs of Exponential Functions	118	(7)
Continuous Growth and the Number e	125	(18)
Review Problems	132	(5)
Check Your Understanding	137	(2)
Tools for Chapter 3: Exponents	139	(4)
Logarithmic Functions	143	(38)
Logarithms and their Properties	144	(7)
Logarithms and Exponential Models	151	(8)
The Logarithmic Function	159	(7)
Logarithmic Scales	166	(15)
Review Problems	176	(3)
Check Your Understanding	179	(2)
Transformations of Functions and their Graphs	181	(50)
Vertical and Horizontal Shifts	182	(9)
Reflections and Symmetry	191	(8)
Vertical Stretches and Compressions	199	(8)
Horizontal Stretches and Compressions	207	(6)
The Family of Quadratic Functions	213	(18)
Review Problems	221	(4)
Check your Understanding	225	(2)
Tools for Chapter 5: Completing the Square	227	(4)
Trigonometric Functions	231	(64)
Introduction to Periodic Functions	232	(6)
The Sine and Cosine Functions	238	(8)
Radians	246	(6)
Graphs of the Sine and Cosine	252	(6)
Sinusoidal Functions	258	(9)
Other Trigonometric Functions	267	(6)
Inverse Trigonometric Functions	273	(22)
Review Problems	282	(3)
Check your Understanding	285	(3)
Tools for Chapter 6: Right Triangles	288	(7)
Trigonometry	295	(46)
General Triangles: Laws of Sines and Cosines	296	(6)
Trigonometric Identities	302	(7)
Sum and Difference Formulas for Sine and Cosine	309	(7)
Trigonometric Models	316	(9)
Polar Coordinates	325	(5)
Complex Numbers and Polar Coordinates	330	(11)
Review Problems	337	(2)
Check Your Understanding	339	(2)
Compositions, Inverses, and Combinations of Functions	341	(34)
Composition of Functions	342	(8)
Inverse Functions	350	(11)
Combinations of Functions	361	(14)
Review Problems	370	(3)
Check Your Understanding	373	(2)
Polynomial and Rational Functions	375	(60)
Power Functions	376	(8)
Polynomial Functions	384	(5)
The Short-run Behavior of Polynomials	389	(7)
Rational Functions	396	(6)
The Short-run Behavior of Rational Functions	402	(8)
Comparing Power, Exponential, and Log Functions	410	(6)
Fitting Exponentials and Polynomials to Data	416	(19)
Review Problems	423	(5)
Check Your Understanding	428	(2)
Tools for Chapter 9: Algebraic Fractions	430	(5)
Vectors and Matrices	435	(40)
Vectors	436	(8)
The Components of a Vector	444	(5)
Application of Vectors	449	(7)
The DOT Product	456	(6)
Matrices	462	(13)
Review Problems	471	(3)
Check Your Understanding	474	(1)
Sequences and Series	475	(28)
Sequences	476	(5)
Defining Functions Using Sums: Arithmetic Series	481	(7)
Finite Geometric Series	488	(5)
Infinite Geometric Series	493	(10)
Review Problems	499	(2)
Check Your Understanding	501	(2)
Parametric Equations and Conic Sections	503	(30)
Parametric Equations	504	(10)
Implicitly Defined Curves and Circles	514	(4)
Ellipses	518	(4)
Hyperbolas	522	(4)
Hyperbolic Functions	526	(7)
Review Problems	530	(1)
Check Your Understanding	531	(2)
Answers to Odd-Numbered Problems	533	(28)
Index	561