Functioning in the Real World, Angielskie [EN](1)
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Gord.3896.FM.pgs 5/2/03 10:34 AM Page i
Functioning
in the
Real World
A Precalculus Experience
Second Edition
Sheldon P. Gordon
Farmingdale State University of
New York
Florence S. Gordon
New York Institute of Technology
Alan C. Tucker
SUNY at Stony Brook
Martha J. Siegel
Towson State University
Boston San Francisco New York
London Toronto Sydney Tokyo Singapore Madrid
Mexico City Munich Paris Cape Town Hong Kong Montreal
Gord.3896.FM.pgs 11/21/03 9:54 AM Page ii
Publisher: Greg Tobin
Managing Editor: Karen Guardino
Sponsoring Editor: Anne Kelly
Project Editor: Rachel Reeve
Production Supervisor: Cindy Cody
Marketing Manager: Becky Anderson
Marketing Coordinator: Julia Coen
Media Producer: Sharon Smith
Prepress Supervisor: Caroline Fell
Senior Designer: Barbara Atkinson
Cover and Interior Designer: Andrea Menza
Production Services: Jenny Bagdigian
Compositor: WestWords Inc.
Art Creation: Techsetters
Cover Photograph: Eyewire/Getty
Dedicated to:
Craig Eric Gordon and Kenneth Scott Gordon,
Our love, our pride, our hope, our joy.
Library of Congress Cataloging-in-Publication Data
Gordon, Sheldon P.
Functioning in the real world : a precalculus experience.— 2nd ed. / Sheldon P.
Gordon, Florence S. Gordon, Alan C. Tucker.
p. cm.
Rev. ed. of: Functioning in the real world / Sheldon P. Gordon . . . [et al.]. c1997.
Includes bibliographical references and index.
ISBN 0-201-38389-6
1. Functions. I. Gordon, Florence S. II. Tucker, Alan, 1943 July 6-
III. Functioning in the real world. IV. Title.
QA331.3.G67 2004
515—dc21
2001056076
This book is based on a portion of the materials developed with the support of the Divi-
sion of Undergraduate Education of the National Science Foundation under grants #USE-
91-50440 and #DUE-9254085 for the Math Modeling/PreCalculus Reform Project.
However, any views expressed are not necessarily those of the Foundation.
Copyright © 2004 Pearson Education, Inc. All rights reserved. No part of this publication may be repro-
duced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical,
photocopying, recording, or otherwise, without the prior written permission of the publisher. Printed in
the United States of America.
1 2 3 4 5 6 7 8 9 10 CRW 06 05 04 03
Gord.3896.FM.pgs 5/2/03 10:34 AM Page iii
Contents
Preface
vii
1
Functions in the Real World
1.1
CHAPTER
Functions Are All Around Us
1
1.2
Describing the Behavior of Functions
8
1.3
Representing Functions Symbolically
18
1.4
Connecting Geometric and Symbolic Representations
25
1.5
Mathematical Models 34
Chapter Summary and Review Problems
39
2
Families of Functions
2.1
CHAPTER
Introduction
43
2.2
Linear Functions
44
2.3
Linear Functions and Data
59
2.4
Exponential Growth Functions
70
2.5
Exponential Decay Functions
87
2.6
Logarithmic Functions
99
2.7
Power Functions
113
2.8
Comparing Rates of Growth and Decay
131
2.9
Inverse Functions 140
Chapter Summary and Review Problems
154
3
Fitting Functions to Data
3.1
CHAPTER
Introduction to Data Analysis
161
3.2
Linear Regression Analysis
164
3.3
Fitting Nonlinear Functions to Data
181
3.4
How to Fit Exponential and Logarithmic Functions to Data
196
3.5
How to Fit Power Functions to Data
208
3.6
How Good is the Fit?
221
3.7
Linear Models with Several Variables 237
Chapter Summary and Review Problems
243
4
Extended Families of Functions
4.1
CHAPTER
Introduction to Polynomial Functions
249
4.2
The Behavior of Polynomial Functions
255
4.3
Modeling with Polynomial Functions
273
iii
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iv
Contents
4.4
The Roots of Polynomial Equations: Real or Complex?
285
4.5
Finding Polynomial Patterns
292
4.6
Building New Functions from Old: Operations on Functions
304
4.7
Building New Functions from Old: Shifting, Stretching, and Shrinking
320
4.8
Using Shifting and Stretching to Analyze Data
331
4.9
The Logistic and Surge Functions
346
Chapter Summary and Review Problems
352
5
Modeling with Difference Equations
5.1
CHAPTER
Eliminating Drugs from the Body
357
5.2
Modeling with Difference Equations
371
5.3
The Logistic or Inhibited Growth Model
385
5.4
Newton’s Laws of Cooling and Heating
407
5.5
Geometric Sequences and their Sums
416
Chapter Summary and Review Problems
425
6
Introduction to Trigonometry
6.1
CHAPTER
The Tangent of an Angle
429
6.2
The Sine and Cosine of an Angle
440
6.3
The Sine, Cosine and Tangent in General
456
6.4
Relationships Among Trigonometric Functions
463
6.5
The Law of Sines and the Law of Cosines
469
Chapter Summary and Review Problems
479
7
Modeling Periodic Behavior
7.1
CHAPTER
Introduction to the Sine and Cosine Functions
483
7.2
Modeling Periodic Behavior with Sine and Cosine
494
7.3
Solving Equations with Sine and Cosine: The Inverse Functions
515
7.4
The Tangent Function
527
Chapter Summary and Review Problems
533
8
More About the Trigonometric Functions
8.1
CHAPTER
Relationships Among Trigonometric Functions
539
8.2
Approximating Sine and Cosine with Polynomials
550
8.3
Properties of Complex Numbers
566
8.4
The Road to Chaos
574
Chapter Summary and Review Problems
581
 Gord.3896.FM.pgs 5/2/03 10:34 AM Page v
Contents
v
9
Geometric Models
9.1
CHAPTER
Introduction to Coordinate Systems
583
9.2
Analytic Geometry
585
9.3
Conic Sections: The Ellipse
595
9.4
Conic Sections: The Hyperbola and the Parabola
606
9.5
Parametric Curves
619
9.6
The Polar Coordinate System
630
9.7
Families of Curves in Polar Coordinates
636
Chapter Summary and Review Problems
644
10
Matrix Algebra and Its Applications
10.1
CHAPTER
Geometric Vectors
649
10.2
Linear Models
659
10.3
Scalar Products
670
10.4
Matrix Multiplication
686
10.5
Gaussian Elimination
700
Chapter Summary and Review Problems
718
11
Probability Models (Available on website only)
11.1
CHAPTER
Introduction to Probability Models
11.2
Binomial Probability and the Binomial Formula
11.3
Using Probability to Investigate Polynomials
11.4
Geometric Probability
11.5
Estimating Areas of Plane Regions
11.6
The Normal Distribution Function
11.7
Waiting Time at a Red Light
11.8
Random Patterns in Chaos
Chapter Summary and Review Problems
12
More About Difference Equations
(Available on website only)
12.1
CHAPTER
Solutions of Difference Equations
12.2
Constructing Solutions of First Order Difference Equations
12.3
Modeling with First Order Non-Homogeneous, Difference Equations
12.4
Financing a Car or a Home
12.5
Solving the Fibonacci and Other Second Order Difference Equations
12.6
The Predator-Prey Model
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