Precalculus With Limits A Graphing Approach 5th Edition

Book Preface

Precalculus with Limits: A Graphing Approach, Fifth Edition. We are pleased to present this new edition of our textbook in which we focus on making the mathematics accessible, supporting student success, and offering teachers flexible teaching options.

Accessible to Students

We have taken care to write this text with the student in mind. Paying careful attention to the presentation, we use precise mathematical language and a clear writing style to develop an effective learning tool. We believe that every student can learn mathematics, and we are committed to providing a text that makes the mathematics of the precalculus course accessible to all students. Throughout the text, solutions to many examples are presented from multiple perspectives—algebraically, graphically, and numerically. The side-byside format of this pedagogical feature helps students to see that a problem can be solved in more than one way and to see that different methods yield the same result. The side-by-side format also addresses many different learning styles.

We have found that many precalculus students grasp mathematical concepts more easily when they work with them in the context of real-life situations. Students have numerous opportunities to do this throughout this text. The Make a Decision feature further connects real-life data and applications and motivates students. It also offers students the opportunity to generate and analyze mathematical models from large data sets. To reinforce the concept of functions, we have compiled all the elementary functions as a Library of Parent Functions, presented in a summary on the endpapers of the text for convenient reference. Each function is introduced at the first point of use in the text with a definition and description of basic characteristics.

We have carefully written and designed each page to make the book more readable and accessible to students. For example, to avoid unnecessary page turning and disruptions to students’ thought processes, each example and corresponding solution begins and ends on the same page.

Supports Student Success

During more than 30 years of teaching and writing, we have learned many things about the teaching and learning of mathematics. We have found that students are most successful when they know what they are expected to learn and why it is important to learn the concepts. With that in mind, we have incorporated a thematic study thread throughout this textbook.

Each chapter begins with a list of applications that are covered in the chapter and serve as a motivational tool by connecting section content to real-life situations. Using the same pedagogical theme, each section begins with a set of section learning objectives—What You Should Learn. These are followed by an engaging real-life application—Why You Should Learn It—that motivates students and illustrates an area where the mathematical concepts will be applied in an example or exercise in the section. The Chapter Summary—What Did You Learn?—at the end of each chapter includes Key Terms with page references and Key Concepts, organized by section, that were covered throughout the chapter. The Chapter Summary serves as a useful study aid for students.

Throughout the text, other features further improve accessibility. Study Tips are provided throughout the text at point-of-use to reinforce concepts and to help students learn how to study mathematics. Explorations reinforce mathematical concepts. Each example with worked-out solution is followed by a Checkpoint, which directs the student to work a similar exercise from the exercise set. The Section Exercises begin with a Vocabulary Check, which gives the students an opportunity to test their understanding of the important terms in the section. A Prerequisites Skills is offered in margin notes throughout the textbook exposition. Reviewing the prerequisite skills will enable students to master new concepts more quickly. Synthesis Exercises check students’ conceptual understanding of the topics in each section. Skills Review Exercises provide additional practice with the concepts in the chapter or previous chapters. Review Exercises, Chapter Tests, and periodic Cumulative Tests offer students frequent opportunities for self-assessment and to develop strong study and test-taking skills. The Progressive Summaries and the Study Capsules serve as a quick reference when working on homework or as a cumulative study aid.

The use of technology also supports students with different learning styles, and graphing calculators are fully integrated into the text presentation. The Technology Support Appendix makes it easier for students to use technology. Technology Support notes are provided throughout the text at point-of-use. These notes guide students to the Technology Support Appendix, where they can learn how to use specific graphing calculator features to enhance their understanding of the concepts presented in the text. These notes also direct students to the Graphing Technology Guide, in the Online Study Center, for keystroke support that is available for numerous calculator models. Technology Tips are provided in the text at point-of-use to call attention to the strengths and weaknesses of graphing technology, as well as to offer alternative methods for solving or checking a problem using technology. Because students are often misled by the limitations of graphing calculators, we have, where appropriate, used color to enhance the graphing calculator displays in the textbook. This enables students to visualize the mathematical concepts clearly and accurately and avoid common misunderstandings.

Numerous additional text-specific resources are available to help students succeed in the precalculus course. These include “live” online tutoring, instructional DVDs, and a variety of other resources, such as tutorial support and self-assessment, which are available on the Web and in Eduspace®. In addition, the Online Notetaking Guide is a notetaking guide that helps students organize their class notes and create an effective study and review tool.