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Overview

Exceptionally accessible and user-friendly, this introduction to precalculus features an abundance of interesting real-world applications that relate to readers' everyday lives. Filled with scenarios, examples, study tips, exercises, etc., it takes the intimidation out of learning precalculus, and gets readers up to speed quickly and painlessly. Prerequisites: Fundamental Concepts of Algebra. Equations, Inequalities, and Mathematical Models. Functions and Graphs. Polynomial and Rational Functions. Exponential and Logarithmic Functions. Trigonometric Functions. Analytic Trigonometry. Additional Topics in Trigonometry. Systems of Equations and Inequalities. Matrices and Determinants. Conic Sections. Sequences, Induction, and Probability. For anyone wanting a user-friendly introduction to precalculus.
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Editorial Reviews

Booknews
This text is designed to help students make the transition into calculus. The goals are to present a solid foundation in algebra and trigonometry and their applications to authentic real-world problems, as well as to enable the development of problem-solving skills and critical thinking. Blitzer (Miami-Dade Community College) discusses fundamental concepts of algebra; equations, inequalities, and mathematical models; functions and graphs; polynomial and rational, exponential and logarithmic, and trigonometric functions; analytic trigonometry and additional topics; systems of equations and inequalities; matrices and determinants; conic sections and analytic geometry; sequences, induction, and probability; and introduction to calculus. Objectives in each chapter appear in boxed sections, with a color illustration. Annotation c. Book News, Inc., Portland, OR (booknews.com)
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Product Details

  • ISBN-13: 9780130281531
  • Publisher: Pearson Education
  • Publication date: 1/18/2001
  • Edition description: Older Edition
  • Edition number: 1
  • Pages: 1166
  • Product dimensions: 8.12 (w) x 10.25 (h) x 1.62 (d)

Read an Excerpt

PREFACE:

Preface

Precalculus is designed and written to help students make the transition into calculus. The book has three fundamental goals:

  1. To help students acquire a solid foundation in algebra and trigonometry, preparing them for calculus;
  2. To show students how algebra and trigonometry can model and solve authentic real-world problems;
  3. To enable students to develop problem-solving skills, fostering critical thinking within a varied and interesting setting.

Precalculus is not simply a condensed version of my Algebra and Trigonometry book. Precalculus students are different from algebra and trigonometry students, and this text reflects those differences. Here are a few specific examples:

  • Factorizations involving fractional and negative exponents, as well as simplifying the kinds of fractional expressions that students encounter in calculus, have been added to Chapter P.
  • Chapter 1 includes applications that are traditional calculus problems and that can be approached algebraically.
  • Chapter 2 includes discussions of difference quotients, average rate of change, average velocity, and composite functions in calculus.
  • Chapter 3 introduces an optimization strategy for solving word problems within the context of quadratic functions. Students will be able to use this strategy in calculus when solving similar problems with the derivative.
  • Chapter 5 develops trigonometry from the perspective of the unit circle.
  • Liberal arts applications are often replaced by more scientific applications. For example, Einstein's relativity models arediscussed in Chapter 1, and Newton's Law of Cooling is developed in Chapter 4.
  • Chapter 12, entitled "Introduction to Calculus," takes the student into calculus with discussions of limits, continuity, and derivatives.

A source of frustration for me and my colleagues is that very few students read their textbook. When I ask students why they do not take full advantage of the text, their responses generally fall into two categories:

  • "I cannot follow the explanations."
  • "The applications are not interesting."

I thought about both of these objections in writing every page of this book.

"I can't follow the explanations." For many of my students, textbook explanations are too compressed. The chapters in Precalculus have been written to make them extremely accessible. Every section contains a range of simple, intermediate, and challenging examples. Voice balloons allow for specific annotations in examples, further clarifying procedures and concepts.

"The applications are not interesting." One of the things I enjoy most about teaching in a large urban community college is the diversity of who my students; are and what interests them. Real-world data that celebrate this variety are used to bring relevance to examples, discussions, and applications. I selected all updated real-world data to be interesting and intriguing to students. By connecting; precalculus to the whole spectrum of their interests, it is my intent to show students that their world is profoundly mathematical and, indeed, pi is in the sky.

Student Supplements

Student Solutions Manual (0-13-028654-0); (2865D-2). Includes fully worked out. solutions to most of the odd-numbered exercises in the text as well as all exercises in chapter tests and all review exercises.

MathPak Integrated Learning Environment (0-13-028247-2); (28246-5). Contains the College Algebra MathPro 4.0 along with a passcode-protected Website: specifically designed to accompany this text. This product combines the series' key' supplements into a comprehensive, easy-to-navigate package. Materials on the Website include but are not limited to: Section-bysection reading quizzes, Section-by-Section Powerpoint downloads, additional chapter projects, Chapter Quizzes and Tests, Student Solutions Manuals presented by chapter (exactly what is in the print version), Chapter Destinations and to interesting math Websites, and Graphing Calculator Manuals for the full line of TI's, Sharp, HP, and Casio Calculators.

Review Videos (0-13-028240-5); (2824K-6). Section-by-section videos written by and highlighting Jacquelyn White of St. Leo College. Each segment covers approximately 20 minutes of the key concepts and examples for each section. Each set of videos comes with a permissions letter allowing the school to duplicate for specific campus needs.

Precalculus Investigations/Simundza, et. (0-13-010954-1); (1095D-6). A three year NSFfunded project integrates an applied approach to the topics in the Precalculus curriculum via applied projects. The investigations reflect the AMATYC and NCTM Standards in both curriculum content and pedagogy.

Companion Website (www.prenhall.com/blitzer). This CW address will lead to the bridge page for all of the Blitzer titles. On the CW sites (which are different than the MathPak sites) are the following: Chapter Quizzes, Chapter Tests, Projects, Graphing Calculator Manual, Destinations, and PowerPoints.

WebCT/Blackboard. Contains all the materials from the MathPak website (i.e., no MathPro) plus testing materials. Can be made available in Blackboard on adoption.

Instructor Supplements

Instructor's Resource Manual (0-13-028656-7) (2865F-7). IRM contains the full solutions to the even-numbered exercises in the text.

TestGen-EQ WIN/MAC CD (0-13-028249-9) (2824J-8). New to Prentice Hall Mathematics is the use of TestGen EQ for our mathematics testing. TestGen-EQ is a fully algorithmic, easy-to-use software program written and based on the section objectives in the text.

Test Item File (0-13-028676-1) (2867F-5). A hard copy version of materials derived from the TestGen-EQ program.

To the Student

I've written this book so that you can learn about the power of algebra and trigonometry and how it relates directly to your life outside the classroom. All concepts are carefully explained, important definitions and procedures are set off in boxes, and worked-out examples that present solutions in a step-by-step manner appear in every section. Each example is followed by a similar matched problem, called a Check Point, for you to try so that you can actively participate in the learning process as you read the book. (Answers to all Check Points appear in the back of the book.) Study Tips offer hints and suggestions and often point out common errors to avoid. A great deal of attention has been given to applying algebra and trigonometry to your life to make your learning experience both interesting and relevant. As you begin your studies, I would like to offer some specific suggestions for using this book and for being successful in this course:

  1. Attend all lectures. No book is intended to be a substitute for valuable insights and interactions that occur in the classroom. In addition to arriving for lecture on time and being prepared, you will find it useful to read the section before it is covered in lecture. This will give you a clear idea of the new material that will be discussed.
  2. Read the book. Read each section with pen (or pencil) in hand. Move through the illustrative examples with great care. These worked-out examples provide a model for doing exercises in the exercise sets. As you proceed through the reading, do not give up if you do not understand every single word. Things will become clearer as you read on and see how various procedures are applied to specific worked-out examples.
  3. Work problems every day and check your answers. The way to learn mathematics is by doing mathematics, which means working the Check Points and assigned exercises in the exercise sets. The more exercises you work, the better you will understand the material.
  4. Prepare for chapter exams. After completing a chapter, study the summary, work the exercises in the Chapter Review, and work the exercises in the Chapter Test. Answers to all these exercises are given in the back of the book.
  5. Use the supplements available with this book. A solutions manual containing worked-out solutions to the book's odd-numbered exercises and all review exercises, a dynamic web page, and video tapes created for every section of the book are among the supplements created to help you tap into the power of mathematics. Ask your instructor or bookstore what supplements are available and where you can find them.

It is my hope that that you will enjoy the pages of this book as you empower yourself with the algebra and trigonometry needed to succeed in calculus, your career, and in your life.

Regards,
Bob
Robert Blitzer

Read More Show Less

Table of Contents

P. Prerequisites: Fundamental Concepts of Algebra.

Real Numbers and Algebraic Expressions. Exponents and Scientific Notation. Radicals and Rational Exponents. Polynomials. Factoring Polynomials. Rational Expressions. Solving Linear Equations. Solving Quadratic Equations. Solving Inequalities.



1. Graphs, Functions, and Models.

Graphs and Graphing Utilities. Lines and Slope. Distance and Midpoint Formulas; Circles. Basics of Functions. Graphs of Functions. Transformations of Functions. Combinations of Functions; Composite Functions. Inverse Functions. Modeling with Functions.



2. Polynomial and Rational Functions.

Complex Numbers. Quadratic Functions. Polynomial Functions and their Graphs. Dividing Polynomials: Remainder and Factor Theorems. Zeros of Polynomial Functions. Rational Functions and Their Graphs. Polynomial and Rational Inequalities. Modeling Using Variation.



3. Exponential and Logarithmic Functions.

Exponential Functions. Logarithmic Functions. Properties of Logarithms. Exponential and Logarithmic Equations. Modeling with Exponential and Logarithmic Functions.



4. Trigonometric Functions.

Angles and Their Measure. Trigonometric Functions: The Unit Circle. Right Triangle Trigonometry. Trigonometric Functions of Any Angle. Graphs of Sine and Cosine Functions. Graphs of other Trigonometric Functions. Inverse Trigonometric Functions. Applications of Trigonometric Functions.



5. Analytic Trigonometry.

Verifying Trigonometric Identities. Sum and Difference Formulas. Double-Angle and Half-Angle Formulas. Product-to Sum and Sum-to Product Formulas. Trigonometric Equations.



6. AdditionalTopics in Trigonometry.

The Law of Sines. The Law of Cosines. Polar Coordinates. Graphs of Polar Equations. Complex Numbers in Polar Form; DeMoivre's Theorem. Vectors. The Dot Product.



7. Systems of Equations and Inequalities.

Systems of Linear Equations in Two Variables. Systems of Linear Equations in Three Variables. Partial Fractions. Systems of Nonlinear Equations in Two Variables. Systems of Inequalities. Linear Programming.



8. Matrices and Determinants.

Matrix Solutions to Linear Systems. Inconsistent and Dependent Systems and Their Applications. Matrix Operations and Their Applications. Multiplicative Inverse of Matrices and Matrix Equations. Determinants and Cramer's Rule.



9. Conic Sections and Analytic Geometry.

The Ellipse. The Hyperbola. The Parabola. Rotation of Axes. Parametric Equations. Conic Sections in Polar Coordinates.



10. Sequences, Induction, and Probability.

Sequences and Summation Notation. Arithmetic Sequences. Geometric Sequences. Mathematical Induction. The Binomial Theorem. Counting Principles, Permutations, and Combinations. Probability.



11. Introduction to Calculus.

Finding Limits Using Tables and Graphs. Finding Limits Using Properties of Limits. One-Sided Limits; Continuous Functions. Introduction to Derivatives.

Read More Show Less

Preface

Preface

Precalculus is designed and written to help students make the transition into calculus. The book has three fundamental goals:

  1. To help students acquire a solid foundation in algebra and trigonometry, preparing them for calculus;
  2. To show students how algebra and trigonometry can model and solve authentic real-world problems;
  3. To enable students to develop problem-solving skills, fostering critical thinking within a varied and interesting setting.

Precalculus is not simply a condensed version of my Algebra and Trigonometry book. Precalculus students are different from algebra and trigonometry students, and this text reflects those differences. Here are a few specific examples:

  • Factorizations involving fractional and negative exponents, as well as simplifying the kinds of fractional expressions that students encounter in calculus, have been added to Chapter P.
  • Chapter 1 includes applications that are traditional calculus problems and that can be approached algebraically.
  • Chapter 2 includes discussions of difference quotients, average rate of change, average velocity, and composite functions in calculus.
  • Chapter 3 introduces an optimization strategy for solving word problems within the context of quadratic functions. Students will be able to use this strategy in calculus when solving similar problems with the derivative.
  • Chapter 5 develops trigonometry from the perspective of the unit circle.
  • Liberal arts applications are often replaced by more scientific applications. For example, Einstein's relativity models are discussed inChapter 1, and Newton's Law of Cooling is developed in Chapter 4.
  • Chapter 12, entitled "Introduction to Calculus," takes the student into calculus with discussions of limits, continuity, and derivatives.

A source of frustration for me and my colleagues is that very few students read their textbook. When I ask students why they do not take full advantage of the text, their responses generally fall into two categories:

  • "I cannot follow the explanations."
  • "The applications are not interesting."

I thought about both of these objections in writing every page of this book.

"I can't follow the explanations." For many of my students, textbook explanations are too compressed. The chapters in Precalculus have been written to make them extremely accessible. Every section contains a range of simple, intermediate, and challenging examples. Voice balloons allow for specific annotations in examples, further clarifying procedures and concepts.

"The applications are not interesting." One of the things I enjoy most about teaching in a large urban community college is the diversity of who my students; are and what interests them. Real-world data that celebrate this variety are used to bring relevance to examples, discussions, and applications. I selected all updated real-world data to be interesting and intriguing to students. By connecting; precalculus to the whole spectrum of their interests, it is my intent to show students that their world is profoundly mathematical and, indeed, pi is in the sky.

Student Supplements

Student Solutions Manual (0-13-028654-0); (2865D-2). Includes fully worked out. solutions to most of the odd-numbered exercises in the text as well as all exercises in chapter tests and all review exercises.

MathPak Integrated Learning Environment (0-13-028247-2); (28246-5). Contains the College Algebra MathPro 4.0 along with a passcode-protected Website: specifically designed to accompany this text. This product combines the series' key' supplements into a comprehensive, easy-to-navigate package. Materials on the Website include but are not limited to: Section-bysection reading quizzes, Section-by-Section Powerpoint downloads, additional chapter projects, Chapter Quizzes and Tests, Student Solutions Manuals presented by chapter (exactly what is in the print version), Chapter Destinations and to interesting math Websites, and Graphing Calculator Manuals for the full line of TI's, Sharp, HP, and Casio Calculators.

Review Videos (0-13-028240-5); (2824K-6). Section-by-section videos written by and highlighting Jacquelyn White of St. Leo College. Each segment covers approximately 20 minutes of the key concepts and examples for each section. Each set of videos comes with a permissions letter allowing the school to duplicate for specific campus needs.

Precalculus Investigations/Simundza, et. (0-13-010954-1); (1095D-6). A three year NSFfunded project integrates an applied approach to the topics in the Precalculus curriculum via applied projects. The investigations reflect the AMATYC and NCTM Standards in both curriculum content and pedagogy.

Companion Website (www.prenhall.com/blitzer). This CW address will lead to the bridge page for all of the Blitzer titles. On the CW sites (which are different than the MathPak sites) are the following: Chapter Quizzes, Chapter Tests, Projects, Graphing Calculator Manual, Destinations, and PowerPoints.

WebCT/Blackboard. Contains all the materials from the MathPak website (i.e., no MathPro) plus testing materials. Can be made available in Blackboard on adoption.

Instructor Supplements

Instructor's Resource Manual (0-13-028656-7) (2865F-7). IRM contains the full solutions to the even-numbered exercises in the text.

TestGen-EQ WIN/MAC CD (0-13-028249-9) (2824J-8). New to Prentice Hall Mathematics is the use of TestGen EQ for our mathematics testing. TestGen-EQ is a fully algorithmic, easy-to-use software program written and based on the section objectives in the text.

Test Item File (0-13-028676-1) (2867F-5). A hard copy version of materials derived from the TestGen-EQ program.

To the Student

I've written this book so that you can learn about the power of algebra and trigonometry and how it relates directly to your life outside the classroom. All concepts are carefully explained, important definitions and procedures are set off in boxes, and worked-out examples that present solutions in a step-by-step manner appear in every section. Each example is followed by a similar matched problem, called a Check Point, for you to try so that you can actively participate in the learning process as you read the book. (Answers to all Check Points appear in the back of the book.) Study Tips offer hints and suggestions and often point out common errors to avoid. A great deal of attention has been given to applying algebra and trigonometry to your life to make your learning experience both interesting and relevant. As you begin your studies, I would like to offer some specific suggestions for using this book and for being successful in this course:

  1. Attend all lectures. No book is intended to be a substitute for valuable insights and interactions that occur in the classroom. In addition to arriving for lecture on time and being prepared, you will find it useful to read the section before it is covered in lecture. This will give you a clear idea of the new material that will be discussed.
  2. Read the book. Read each section with pen (or pencil) in hand. Move through the illustrative examples with great care. These worked-out examples provide a model for doing exercises in the exercise sets. As you proceed through the reading, do not give up if you do not understand every single word. Things will become clearer as you read on and see how various procedures are applied to specific worked-out examples.
  3. Work problems every day and check your answers. The way to learn mathematics is by doing mathematics, which means working the Check Points and assigned exercises in the exercise sets. The more exercises you work, the better you will understand the material.
  4. Prepare for chapter exams. After completing a chapter, study the summary, work the exercises in the Chapter Review, and work the exercises in the Chapter Test. Answers to all these exercises are given in the back of the book.
  5. Use the supplements available with this book. A solutions manual containing worked-out solutions to the book's odd-numbered exercises and all review exercises, a dynamic web page, and video tapes created for every section of the book are among the supplements created to help you tap into the power of mathematics. Ask your instructor or bookstore what supplements are available and where you can find them.

It is my hope that that you will enjoy the pages of this book as you empower yourself with the algebra and trigonometry needed to succeed in calculus, your career, and in your life.

Regards,
Bob
Robert Blitzer

Read More Show Less

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