Barnett/Ziegler/Byleen - Precalculus: Functions and Graphs, 4/e

Features

Precalculus: Functions and Graphs is one of three books in the authors' precalculus series. Improvements in this edition evolved out of the generous response from a large number of users of the last and previous editions as well as survey results from instructors, mathematics departments, course outlines, and college catalogs. Fundamental to a book's growth and effectiveness is classroom use and feedback. Now in its fourth edition, Precalculus: Functions and Graphs has had the benefit of having a substantial amount of both.

Emphasis and Style
The text is written for student comprehension. Great care has been taken to write a book that is mathematically correct and accessible to students. Emphasis is on computational skills, ideas, and problem-solving rather than mathematical theory. Most derivations and proofs are omitted except where their inclusion adds significant insight into a particular concept. General concepts and results are usually presented only after particular cases have been discussed.

Examples and Matched Problems
Over 375 completely worked examples are used to introduce concepts and to demonstrate problem-solving techniques. Each example is followed by a similar matched problem for the student to work while reading the material. This actively involves the student in the learning process. The answers to these matched problems are included at the end of each section for easy reference.

Exploration, Discussion and Group Activities
Every section contains Explore-Discuss boxes interspersed at appropriate places to encourage a student to think about a relationship or process before a result is stated or to investigate additional consequences of a development in the text. Verbalization of mathematical concepts, results, and processes is encouraged in these Explore-Discuss boxes, as well as in some matched problems, and in particular problems in almost every exercise set. The Explore-Discuss material can also be used as an in-class or out-of-class group activity. In addition, at the end of every chapter, before the chapter review, is a special chapter group activity that involves a number of the concepts discussed in the chapter. All of these special activities are highlighted to emphasize their importance.

Exercise Sets
The book contains over 5600 problems. Each exercise set is designed so that an average or below-average student will experience success and a very capable student will be challenged. Exercise sets are mostly divided into A (routine, easy mechanics), B (more difficult mechanics), C (difficult mechanics and some theory) level, and Applications. The most difficult application problems are marked with two stars (**), the moderately difficult application problems with one star (*), and the easier application problems are not marked.

Applications
One of the primary objectives of this book is to give the student substantial experience in modeling and solving real world problems. Enough applications are included to convince even the most skeptical student that mathematics is really useful. An Applications Index is included to help locate particular applications. Most of the applications are simplified versions of actual real-world problems taken from professional journals and professional books. No specialized experience is required to solve any of the applications.

Because many students use this book to prepare for calculus, examples and exercises that are especially pertinent to calculus are marked with the icon [ ( ].

Technology
The generic term "graphing utility" is used to refer to any of the various graphing calculators or computer software packages that might be available to a student using this book. Although use of a graphing utility is optional, it is likely that many students and instructors will want to make use of one of these devices. To assist these students and instructors, optional graphing utility activities are included throughout the book beginning in Chapter 3. These include brief discussions in the text, examples or portions of examples solved on a graphing utility, and problems for the student to solve. All of the optional graphing utility material is clearly identified by a blue calculator icon and can be omitted without loss of continuity, if desired.

Graphs and Illustrations
All graphs and illustrations in this edition of the text are new. All of the graphs are computer generated to insure mathematical accuracy. Graphing utility screens displayed in the text are actual output from a graphing calculator.

Important Student Aids
Annotation of examples and developments, in small color type, is found throughout the text to help students through critical stages. Think boxes (dashed boxes) are used to enclose steps that are usually performed mentally. Screened boxes are used to highlight important definitions, theorems, results, and step-by-step processes. Caution boxes appear throughout the text where student errors often occur (see Section 1-7). Functional use of four colors improves the clarity of many illustrations, graphs, and developments, and guides students through certain critical steps. Boldface type is used to introduce new terms and highlight important comments. Chapter review sections include a review of all important terms and symbols and a comprehensive review exercise. Cumulative review exercises after every second or third chapter provide additional practice for students. Answers to review exercises, keyed to appropriate sections, are included in the back of the book. Answers to all other odd-numbered problems are also in the back of the book. Summaries of formulas and symbols (keyed to the sections in which they are introduced) are found inside the front and back covers of the text for convenient reference.

Principal Changes from the Third Edition
As mentioned earlier, exploration and discussion activities have been distributed uniformly throughout the book. These new elements include Explore-Discuss questions in the text and exercise sets, and chapter group activities. The optional material on graphing utilities is also more uniformly distributed.

In Chapter 1, linear equations and their applications are now covered in one section and a new section on systems of linear equations and their applications has been added.

In Chapter 2, the sections on aids to graphing functions and operations on functions have been combined to present these related topics in a more concise fashion. The section on rational functions has been moved to Chapter 3.

The material in Chapter 3 has been extensively revised and reorganized, due in no small part to the effect that graphing utilities have had on some of these topics. Section 3-2 now deals with techniques for finding exact zeros, including all rational zeros, and Section 3-3 covers approximating real zeros.

In Chapter 6, techniques for solving trigonometric equations have been condensed into a single section, again reflecting some of the impact that technology has had on equation solving. The treatment of polar coordinates and polar graphs has also been condensed into a single section in Chapter 7.

Since solving two linear equations in two variables is now covered in Chapter 1, the first section of Chapter 8 now concentrates on graphical methods and matrix methods. In Chapter 9, matrix addition and multiplication are now covered in a single section.

Counting techniques have been moved to Chapter 10 and the remaining probability material has been deleted.

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