Precalculus: Graphing and Data Analysis

Precalculus: Graphing and Data Analysis

Paperback(2ND SOL MN)

$33.33

Overview

This book motivates students by highlighting real people facing real challenges finding real solutions. This series features real workers at Motorola, along with hundreds of applications and real data sets highlighting the relevance and scope of activities a reader may encounter in life. Covers such topics as graphs, functions, polynomial and rational functions, the zeros of a polynomial function, exponential and logarithmic functions, trigonometric functions, analytic trigonometry, applications of trigonometric functions, polar coordinates, vectors, analytic geometry, systems of equations and inequalities, sequence, induction, the binomial theorem, counting and probability, and more. For anyone interested in Precalculus.

Product Details

ISBN-13: 9780130287595
Publisher: Pearson
Publication date: 09/28/2000
Edition description: 2ND SOL MN
Pages: 736
Product dimensions: 7.99(w) x 10.00(h) x (d)

Read an Excerpt

PREFACE:

PREFACE TO THE INSTRUCTOR

As professors at respectively an urban public university and a community college, Michael Sullivan and Michael Sullivan III are aware of the varied needs of Precalculus students, ranging from those having little mathematical background and fear of mathematics courses to those who have had a strong mathematical education and are highly motivated. For some of your students, this will be their last course in mathematics, while others might decide to further their mathematical education. This text is written for both groups. As the author of precalculus, engineering calculus, finite math, and business calculus texts, and as a teacher, Michael understands what students must know if they are to be focused and successful in upper level math courses. However, as a father of four, including the co-author, he also understands the realities of college life. Michael Sullivan III believes passionately in the value of technology as a tool for learning that enhances understanding without sacrificing important skills. Both authors have taken great pains to insure that the text contains solid, student-friendly examples and problems, as well as a clear and seamless writing style. We encourage you to share with us your experiences teaching from this text.

In the Second Edition

The second edition builds upon a strong foundation by integrating new features and techniques that further enhance student interest and involvement. The elements of the previous edition that have proved successful remain, while many changes, some obvious, others subtle, have been made. The text has been streamlined to increase accessibility. A huge benefitof authoring a successful series is the broad-based feedback upon which improvements and additions are ultimately based. Virtually every change to this edition is the result of thoughtful comments and suggestions made by colleagues and students who have used the previous edition. This feedback has proved invaluable and has been used to make changes that improve the flow and usability of the text. For example, some topics have been moved to better reflect the way teachers approach the course. One significant change is the inclusion of the "Field Trip to Motorola" chapter projects. These projects take the incorporation of real life in mathematics to a higher level. The supplements package has been enhanced through upgrading traditional supplements and adding innovative media components such as MathPak, an Integrated Learning Environment. MathPak combines all of the text's key supplements into one easy-to-navigate software package.

Changes to the Second Edition

Chapter 1
• "Data in Ordered Pairs" has been moved to the section where linear curve fitting is introduced.
• "Circles" is now covered in a stand-alone section.
• The section on inequalties now contains a discussion of interval notation.

Chapter 2
• "More about Functions" has been divided into "Characteristics of Functions" and "Library of Function: Piecewise Defined Functions".

Chapters 3 & 4
• Chapter 3 has been divided into two parts: Polynomial and Rational Functions and the Zeros of a Polynomial Function.
• The section on Rational Functions has been split into two sections making the material more manageable.

Chapter 5
• Chapter 4 of the 1st Edition. Certain types of exponential and logarithmic equations appear earlier in the chapter.

Chapter 6
• A rewrite of the introduction to trigonometric functions makes the distinction between the functions of a real number and that of an angle clearer.
• The section on graphing of trigonometric functions is divided in two sections—one graphing the sine and cosine functions and the other graphing the four remaining trigonometric functions.
• The section on Inverse Trigonometric Functions have been moved to Chapter 7.
• The section on Right Triangle Trigonometry now appears in Chapter 8.

Chapter 7
• Now includes two sections on the section on the Inverse Trigonometric Functions and two section on Trigonometric Equations.

Chapter 8
• The first section discusses right triangle trigonometry and applications.

Chapter 9
• Static equilibrium problems were added.
• This chapter now includes a new section on the cross product.

Chapter 10
• Asymptotes are introduced earlier in the section on hyperbolas.

Chapter 11
• Now includes two introductory sections on systems of linear equations.
• The section on determinants includes a discussion on minors and cofactors.
• Systems of Inequalities and Linear Programming are combined into one section.

Chapter 12
• The first five sections of Chapter 11 from the first edition.
• The section on sequences utilizes the power of recursive functions and the graphing calculator to discuss amortization.

Chapter 13
• The second part of Chapter 11 from the 1st Edition.
• Now contains two sections on probability: classical and empirical.

Chapter 14
• A new section on the Area Problem; the Integral has been added.

Appendix
• Rewritten to provide a more thorough review of prerequisite material.
• Can be used as a "just-in-time" review by students.

PREFACE TO THE STUDENT

As you begin your study of Precalculus, you may feel overwhelmed by the number of theorems, definitions, procedures, and equations that confront you. You may even wonder whether or not you can learn all of this material in the time allotted. These concerns are normal. Keep in mind that many elements of Precalculus are all around us as we go through our daily routines. Many of the concepts you will learn to express mathematically, you already know intuitively. For many of you, this may be your last math course, while for others, it is just the first in a series of many. Either way, this text was written with you in mind. One of the coauthors, Michael Sullivan, has taught Precalculus courses for over thirty years. He is also the father of four college graduates, including this text's other co-author, who called home from time to time frustrated and with questions. We both know what you're going through. So we have written a text that doesn't overwhelm, or unnecessarily complicate Precalculus, but at the same time gives you the skills and practice you need to be successful.

This text is designed to help you the student, master the terminology and basic concepts of Precalculus. These aims have helped to shape every aspect of the book. Many learning aids are built into the format of the text to make your study of the material easier and more rewarding. This book is meant to be a "machine for learning," that can help you focus your efforts and get the most from the time and energy you invest.

Please do not hesitate to contact us through Prentice Hall with any suggestions or comments that would improve this text.

Best Wishes!
Michael Sullivan
Michael Sullivan, III

Table of Contents

Preface vii
Graphs and Equations
Rectangular Coordinates; Graphing Utilities
1(6)
Graphs of Equations
7(6)
Solving Equations
13(7)
Setting Up Equations: Applications
20(11)
Solving Inequalities
31(11)
Lines
42(6)
Scatter Diagrams; Linear Curve Fitting
48(4)
Circles
52(18)
Chapter Review
57(13)
Functions
Functions
70(9)
Characteristics of Functions
79(7)
Library of Functions; Piecewise Defined Functions
86(4)
Graphing Techniques: Transformations
90(9)
Operations on Functions; Composite Functions
99(8)
Mathematical Models: Constructing Functions
107(14)
Chapter Review
113(8)
Polynomial and Rational Functions
Quadratic Functions; Curve Fitting
121(12)
Power Functions; Curve Fitting
133(2)
Polynomial Functions; Curve Fitting
135(7)
Rational Functions I
142(3)
Rational Functions II
145(27)
Chapter Review
161(11)
The Zeros of a Polynomial Function
The Real Zeros of a Polynomial Function
172(19)
Complex Numbers: Quadratic Equations with a Negative Discriminant
191(3)
Complex Zeros; Fundamental Theorem of Algebra
194(6)
Polynomial and Rational Inequalities
200(30)
Chapter Review
218(12)
Exponential and Logarithmic Functions
One-to-One Functions; Inverse Functions
230(9)
Exponential Functions
239(7)
Logarithmic Functions
246(7)
Properties of Logarithms
253(4)
Logarithmic and Exponential Equations
257(5)
Compound Interest
262(4)
Growth and Decay
266(5)
Exponential, Logarithmic, and Logistic Curve Fitting
271(12)
Chapter Review
276(7)
Trigonometric Functions
Angles and Their Measure
283(4)
Trigonometric Functions: Unit Circle Approach
287(10)
Properties of the Trigonometric Functions
297(7)
Graphs of the Sine and Cosine Functions
304(2)
Graphs of the Tangent, Cotangent, Cosecant, and Secant Functions
306(2)
Sinusoidal Graphs; Sinusoidal Curve Fitting
308(18)
Chapter Review
317(9)
Analytic Trignometry
Trigonometric Identities
326(4)
Sum and Difference Formulas
330(5)
Double-Angle and Half-Angle Formulas
335(7)
Product-to-Sum and Sum-to-Product Formulas
342(3)
The Inverse Trigonometric Functions (I)
345(4)
The Inverse Trigonometric Functions (II)
349(9)
Trigonometric Equations (I)
358(3)
Trigonometric Equations (II)
361(18)
Chapter Review
368(11)
Applications of Trigonometric Functions
Right Triangle Trigonometry
379(8)
The Law of Sines
387(6)
The Law of Cosines
393(7)
The Area of a Triangle
400(4)
Simple Harmonic Motion; Damped Motion
404(11)
Chapter Review
408(7)
Polar Coordinates; Vectors
Polar Coordinates
415(4)
Polar Equations and Graphs
419(13)
The Complex Plane; DeMoivre's Theorem
432(6)
Vectors
438(5)
The Dot Product
443(4)
Vectors in Space
447(4)
The Cross Product
451(14)
Chapter Review
456(9)
Analytic Geometry
The Parabola
465(8)
The Ellipse
473(9)
The Hyperbola
482(10)
Rotation of Axes; General Form of a Conic
492(8)
Polar Equations of Conics
500(5)
Plane Curves and Parametric Equations
505(20)
Chapter Review
513(12)
Systems of Equations and Inequalities
Systems of Linear Equations: Two Equations Containing Two Unknowns
525(7)
Systems of Linear Equations: Three Equations Containing Three Unknonws
532(6)
Systems of Linear Equations: Matrices
538(11)
Systems of Linear Equations: Determinants
549(12)
Matrix Algebra
561(7)
Partial Fraction Decomposition
568(8)
Systems of Nonlinear Equations
576(20)
Systems of Linear Inequalities; Linear Programming
596(39)
Chapter Review
614(21)
Sequences; Induction; The Binomial Theorem
Sequences
635(5)
Arithmetic Sequences
640(4)
Geometric Sequences; Geometric Series
644(5)
Mathematical Induction
649(3)
The Binomial Theorem
652(10)
Chapter Review
655(7)
Counting and Probability
Sets and Counting
662(2)
Permutations and Combinations
664(3)
Probability
667(4)
Analyzing Univariate Data; Probabilities from Data
671(6)
Chapter Review
674(3)
A Preview of Calculus: The Limit, Derivative, and Integral of a Function
Finding Limits Using Tables and Graphs
677(3)
Algebraic Techniques for Finding Limits
680(2)
One-Sided Limits; Continuous Functions
682(5)
The Tangent Problem; The Derivative
687(4)
The Area Problem; The Integral
691(14)
Chapter Review
697(8)
Appendix
1 Topics from Algebra
705(2)
2 Integer Exponents
707(2)
3 Polynomials
709(2)
4 Polynomial Division; Synthetic Division
711(5)
5 Factoring
716(2)
6 Solving Equations
718(1)
7 Rational Expressions
719(4)
8 Radicals; Rational Exponents
723(2)
9 Geometry Review
725(2)
10 Completing the Square; The Quadratic Formula
727

Preface

PREFACE:

PREFACE TO THE INSTRUCTOR

As professors at respectively an urban public university and a community college, Michael Sullivan and Michael Sullivan III are aware of the varied needs of Precalculus students, ranging from those having little mathematical background and fear of mathematics courses to those who have had a strong mathematical education and are highly motivated. For some of your students, this will be their last course in mathematics, while others might decide to further their mathematical education. This text is written for both groups. As the author of precalculus, engineering calculus, finite math, and business calculus texts, and as a teacher, Michael understands what students must know if they are to be focused and successful in upper level math courses. However, as a father of four, including the co-author, he also understands the realities of college life. Michael Sullivan III believes passionately in the value of technology as a tool for learning that enhances understanding without sacrificing important skills. Both authors have taken great pains to insure that the text contains solid, student-friendly examples and problems, as well as a clear and seamless writing style. We encourage you to share with us your experiences teaching from this text.

In the Second Edition

The second edition builds upon a strong foundation by integrating new features and techniques that further enhance student interest and involvement. The elements of the previous edition that have proved successful remain, while many changes, some obvious, others subtle, have been made. The text has been streamlined to increase accessibility. A hugebenefitof authoring a successful series is the broad-based feedback upon which improvements and additions are ultimately based. Virtually every change to this edition is the result of thoughtful comments and suggestions made by colleagues and students who have used the previous edition. This feedback has proved invaluable and has been used to make changes that improve the flow and usability of the text. For example, some topics have been moved to better reflect the way teachers approach the course. One significant change is the inclusion of the "Field Trip to Motorola" chapter projects. These projects take the incorporation of real life in mathematics to a higher level. The supplements package has been enhanced through upgrading traditional supplements and adding innovative media components such as MathPak, an Integrated Learning Environment. MathPak combines all of the text's key supplements into one easy-to-navigate software package.

Changes to the Second Edition

Chapter 1
• "Data in Ordered Pairs" has been moved to the section where linear curve fitting is introduced.
• "Circles" is now covered in a stand-alone section.
• The section on inequalties now contains a discussion of interval notation.

Chapter 2
• "More about Functions" has been divided into "Characteristics of Functions" and "Library of Function: Piecewise Defined Functions".

Chapters 3 & 4
• Chapter 3 has been divided into two parts: Polynomial and Rational Functions and the Zeros of a Polynomial Function.
• The section on Rational Functions has been split into two sections making the material more manageable.

Chapter 5
• Chapter 4 of the 1st Edition. Certain types of exponential and logarithmic equations appear earlier in the chapter.

Chapter 6
• A rewrite of the introduction to trigonometric functions makes the distinction between the functions of a real number and that of an angle clearer.
• The section on graphing of trigonometric functions is divided in two sections—one graphing the sine and cosine functions and the other graphing the four remaining trigonometric functions.
• The section on Inverse Trigonometric Functions have been moved to Chapter 7.
• The section on Right Triangle Trigonometry now appears in Chapter 8.

Chapter 7
• Now includes two sections on the section on the Inverse Trigonometric Functions and two section on Trigonometric Equations.

Chapter 8
• The first section discusses right triangle trigonometry and applications.

Chapter 9
• Static equilibrium problems were added.
• This chapter now includes a new section on the cross product.

Chapter 10
• Asymptotes are introduced earlier in the section on hyperbolas.

Chapter 11
• Now includes two introductory sections on systems of linear equations.
• The section on determinants includes a discussion on minors and cofactors.
• Systems of Inequalities and Linear Programming are combined into one section.

Chapter 12
• The first five sections of Chapter 11 from the first edition.
• The section on sequences utilizes the power of recursive functions and the graphing calculator to discuss amortization.

Chapter 13
• The second part of Chapter 11 from the 1st Edition.
• Now contains two sections on probability: classical and empirical.

Chapter 14
• A new section on the Area Problem; the Integral has been added.

Appendix
• Rewritten to provide a more thorough review of prerequisite material.
• Can be used as a "just-in-time" review by students.

PREFACE TO THE STUDENT

As you begin your study of Precalculus, you may feel overwhelmed by the number of theorems, definitions, procedures, and equations that confront you. You may even wonder whether or not you can learn all of this material in the time allotted. These concerns are normal. Keep in mind that many elements of Precalculus are all around us as we go through our daily routines. Many of the concepts you will learn to express mathematically, you already know intuitively. For many of you, this may be your last math course, while for others, it is just the first in a series of many. Either way, this text was written with you in mind. One of the coauthors, Michael Sullivan, has taught Precalculus courses for over thirty years. He is also the father of four college graduates, including this text's other co-author, who called home from time to time frustrated and with questions. We both know what you're going through. So we have written a text that doesn't overwhelm, or unnecessarily complicate Precalculus, but at the same time gives you the skills and practice you need to be successful.

This text is designed to help you the student, master the terminology and basic concepts of Precalculus. These aims have helped to shape every aspect of the book. Many learning aids are built into the format of the text to make your study of the material easier and more rewarding. This book is meant to be a "machine for learning," that can help you focus your efforts and get the most from the time and energy you invest.

Please do not hesitate to contact us through Prentice Hall with any suggestions or comments that would improve this text.

Best Wishes!
Michael Sullivan
Michael Sullivan, III

Customer Reviews

Most Helpful Customer Reviews

See All Customer Reviews