Precalculus (5th Edition)

1413 Pages·2013·45.656 MB·English

by  Robert F. Blitzer

5
th
EDITION

Robert Blitzer
Miami Dade College
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Library of Congress Cataloging-in-Publication Data
Blitzer, Robert.
Precalculus / Robert Blitzer Miami Dade College. —Fifth edition.
pages cm
Includes index.
ISBN 978-0-321-83734-9
1. Algebra—Textbooks. I. Title.
QA154.3.B586 2014
512—dc23
2012042264
Copyright © 2014, 2010, 2007 Pearson Education, Inc.
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1 2 3 4 5 6 7 8 9 10–DOW–16 15 14 13 12

ISBN 10: 0-321-83734-7
www.pearsonhighered.com ISBN 13: 978-0-321-83734-9
DEDICATION
For Jerid (1985–2012)
And for those who have loved their pets
and have been loved by them
CONTENTS
Preface v iii 1 .5 More on Slope 203
Acknowledgments xii Mid-Chapter Check Point 214
Dynamic Resources xiii 1.6 Transformations of Functions 215
To the Student xv 1 .7 Combinations of Functions; Composite Functions 231
About the Author xvi 1 .8 Inverse Functions 245
Applications Index x vii 1.9 Distance and Midpoint Formulas; Circles 257
1.10 Modeling with Functions 266
P Prerequisites: Fundamental
Summary, Review, and Test 281
Concepts of Algebra 1
Review Exercises 284
P.1 Algebraic Expressions, Mathematical Models, and Real Chapter 1 Test 289
Numbers 2
P.2 Exponents and Scientifi c Notation 20
P .3 Radicals and Rational Exponents 32
P .4 Polynomials 48
P.5 Factoring Polynomials 58
Mid-Chapter Check Point 70
P.6 Rational Expressions 71
P.7 Equations 86
P.8 Modeling with Equations 106
P .9 Linear Inequalities and Absolute Value Inequalities 120
Summary, Review, and Test 134
Review Exercises 135
Chapter P Test 138
1 Functions
and Graphs 141
1.1 Graphs and Graphing Utilities 142
1.2 Basics of Functions and Their Graphs 154
1.3 More on Functions and Their Graphs 173
1.4 Linear Functions and Slope 188
iv
Contents v
3 Exponential and
Logarithmic Functions 413
3.1 Exponential Functions 414
3.2 Logarithmic Functions 427
3.3 Properties of Logarithms 441
Mid-Chapter Check Point 451
3.4 Exponential and Logarithmic Equations 451
3.5 Exponential Growth and Decay; Modeling Data 466
Summary, Review, and Test 482
Review Exercises 484
Chapter 3 Test 488
Cumulative Review Exercises (Chapters P–3) 489
4 Trigonometric
Functions 491
4.1 Angles and Radian Measure 492
4.2 Trigonometric Functions: The Unit Circle 508
4.3 Right Triangle Trigonometry 523
2 Polynomial and 4 .4 Trigonometric Functions of Any Angle 537
Rational Functions 291 Mid-Chapter Check Point 549
4.5 Graphs of Sine and Cosine Functions 551
2.1 Complex Numbers 292
4.6 Graphs of Other Trigonometric Functions 572
2.2 Quadratic Functions 300
4.7 Inverse Trigonometric Functions 585
2 .3 Polynomial Functions and Their Graphs 317
4 .8 Applications of Trigonometric Functions 601
2.4 Dividing Polynomials; Remainder and Factor
Theorems 334 Summary, Review, and Test 612
2.5 Zeros of Polynomial Functions 346 Review Exercises 615
Mid-Chapter Check Point 360 Chapter 4 Test 618
2.6 Rational Functions and Their Graphs 361 Cumulative Review Exercises (Chapters P–4) 619
2.7 Polynomial and Rational Inequalities 381
2.8 Modeling Using Variation 394
Summary, Review, and Test 404
Review Exercises 406
Chapter 2 Test 410
Cumulative Review Exercises (Chapters P–2) 412
6.6 Vectors 739
6.7 The Dot Product 754
Summary, Review, and Test 764
Review Exercises 766
Chapter 6 Test 769
Cumulative Review Exercises (Chapters P–6) 769
5 Analytic
Trigonometry 621 7 Systems of Equations
and Inequalities 771
5.1 Verifying Trigonometric Identities 622
5.2 Sum and Difference Formulas 633 7.1 Systems of Linear Equations in Two Variables 772
5 .3 Double-Angle, Power-Reducing, 7.2 Systems of Linear Equations in Three Variables 792
and Half-Angle Formulas 644
7.3 Partial Fractions 800
Mid-Chapter Check Point 655
7.4 Systems of Nonlinear Equations in Two Variables 811
5.4 Product-to-Sum and Sum-to-Product Formulas 656
Mid-Chapter Check Point 821
5.5 Trigonometric Equations 664
7.5 Systems of Inequalities 822
Summary, Review, and Test 677
7 .6 Linear Programming 835
Review Exercises 678
Summary, Review, and Test 843
Chapter 5 Test 680
Review Exercises 844
Cumulative Review Exercises (Chapters P–5) 680
Chapter 7 Test 846
Cumulative Review Exercises (Chapters P–7) 847
6 Additional Topics
in Trigonometry 681
8 Matrices
6.1 The Law of Sines 682
and Determinants 849
6 .2 The Law of Cosines 694
8.1 Matrix Solutions to Linear Systems 850
6.3 Polar Coordinates 702
8.2 Inconsistent and Dependent Systems and Their
6 .4 Graphs of Polar Equations 714
Applications 862
Mid-Chapter Check Point 725
8.3 Matrix Operations and Their Applications 872
6.5 Complex Numbers in Polar Form; DeMoivre’s
Mid-Chapter Check Point 887
Theorem 726
vi
Contents vii
8.4 Multiplicative Inverses of Matrices and Matrix 9.5 Parametric Equations 974
Equations 888
9.6 Conic Sections in Polar Coordinates 984
8.5 Determinants and Cramer’s Rule 902
Summary, Review, and Test 994
Summary, Review, and Test 914
Review Exercises 996
Review Exercises 915
Chapter 9 Test 998
Chapter 8 Test 918
Cumulative Review Exercises (Chapters P–9) 999
Cumulative Review Exercises (Chapters P–8) 918
10 Sequences, Induction,
9 Conic Sections and
and Probability 1001
Analytic Geometry 919
10.1 Sequences and Summation Notation 1002
9.1 The Ellipse 920
10.2 Arithmetic Sequences 1013
9.2 The Hyperbola 933
10.3 Geometric Sequences and Series 1023
9.3 The Parabola 948
Mid-Chapter Check Point 1039
Mid-Chapter Check Point 960
10.4 Mathematical Induction 1040
9.4 Rotation of Axes 962
1 0.5 The Binomial Theorem 1048
10.6 Counting Principles, Permutations, and
Combinations 1056
10.7 Probability 1067
Summary, Review, and Test 1082
Review Exercises 1084
Chapter 10 Test 1087
Cumulative Review Exercises (Chapters P–10) 1088
11 Introduction to
Calculus 1091
11.1 Finding Limits Using Tables and Graphs 1092
11.2 Finding Limits Using Properties of Limits 1104
11.3 Limits and Continuity 1117
Mid-Chapter Check Point 1124
11.4 Introduction to Derivatives 1125
Summary, Review, and Test 1138
Review Exercises 1139
Chapter 11 Test 1140
Cumulative Review Exercises (Chapters P–11) 1141

Appendix A: Where Did That Come From? Selected Proofs 1143
Appendix B: The Transition from Precalculus to Calculus 1149
Answers to Selected Exercises AA1
Subject Index I1
Photo Credits C1
PREFACE
I’ve written P recalculus, Fifth Edition , to help diverse with Functions) that is not includeedd
students, with different backgrounds and future goals, to in Algebra and Trigonometry.
succeed. The book has three fundamental goals: Modeling skills are applied to
situations that students are likely
1. To help students acquire a solid foundation in algebra
to see in calculus when solving
and trigonometry, preparing them for other courses such
applied problems involving maximmuummm
as calculus, business calculus, and fi nite mathematics.
or minimum values.
2. To show students how algebra and trigonometry can
• Precalculus develops trigonometryy
model and solve authentic real-world problems.
from the perspective of the unit circcllee
3. To enable students to develop problem-solving skills, while (4.2: Trigonometric Functions: Thee UUnniitt
fostering critical thinking, within an interesting setting. Circle). In Algebra and Trigonomeettrryy,,
trigonometry is developed using rigghhtt
One major obstacle in the way of achieving these goals
triangles.
is the fact that very few students actually read their
textbook. This has been a regular source of frustration • Precalculus contains a chapter
for me and for my colleagues in the classroom. Anecdotal (Chapter 11: Introduction to
evidence gathered over years highlights two basic reasons Calculus) that takes the student into calculus with
that students do not take advantage of their textbook: discussions of limits, continuity, and derivatives. This
chapter is not included in Algebra and Trigonometry.
• “I’ll never use this information.”
• Many of the liberal arts applications in Algebra and
• “I can’t follow the explanations.”
Trigonometry are replaced by more scientific or higher
I’ve written every page of the Fifth Edition with the intent level applications in Precalculus. Some examples:
of eliminating these two objections. The ideas and tools • Black Holes in Space (P.2: Exponents and Scientific
I’ve used to do so are described for the student in Notation)
“A Brief Guide to Getting the Most from This Book,”
• Average Velocity (1.5: More on Slope)
which appears at the front of the book.
• Newton’s Law of Cooling (3.5: Exponential Growth
and Decay; Modeling Data)
How Does Precalculus Differ
• Modeling Involving Mixtures and Uniform Motion
from Algebra and Trigonometry?
(7.1: Systems of Linear Equations in Two Variables)
Precalculus is not simply a condensed version of my
Algebra and Trigonometry book. Precalculus students are
What’s New in the Fifth Edition?
different from algebra and trigonometry students, and this
text reflects those differences. Here are a few examples: New Applications and Real-World Data. I’m on a
constant search for data that can be used to illustrate
• Algebra and Trigonometry devotes an entire chapter unique mathematical applications. I researched hundreds
to linear equations, rational equations, quadratic of books, magazines, newspapers, almanacs, and online
equations, radical equations, linear inequalities, and sites to prepare the Fifth Edition. Among the 108
developing models involving these equations and worked-out examples and exercises based on new data
inequalities. Precalculus reviews these topics sets, you’ll find applications involving modeling blood-
in three sections of the prerequisites alcohol concentration (Section P.1), starting salaries for
chapter (P.7: Equations; P.8: college graduates (Section P.8), the world’s vanishing tiger
Modeling with Equations; population (Section 2.3), and the year humans become
P.9: Linear Inequalities and immortal (Section 3.1).
Absolute Value Inequalities).
Functions, the core of any Concept and Vocabulary Checks. The Fifth Edition
contains 679 new short-answer exercises, mainly fill-
precalculus course, are then
in-the-blank and true/false items, that assess students’
introduced in Chapter 1.
understanding of the definitions and concepts presented
• Precalculus contains a
in each section. The Concept and Vocabulary Checks
section on constructing
appear as separate features preceding the Exercise Sets.
functions from verbal
descriptions and Great Question! This feature takes the content of each
formulas (1.10: Modeling Study Tip in the Fourth Edition and presents it in the
viii