Precalculus (6th Edition)

Book Preface

I’ve written Precalculus, Sixth Edition, to help diverse students, with different backgrounds and future goals, to succeed. The book has three fundamental goals:

1. To help students acquire a solid foundation in algebra and trigonometry, preparing them for other courses such as calculus, business calculus, and  nite mathematics.

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, while fostering critical thinking, within an interesting setting. One major obstacle in the way of achieving these goals is the fact that very few students actually read their textbook. This has been a regular source of frustration for me and for my colleagues in the classroom. Anecdotal evidence gathered over years highlights two basic reasons that students do not take advantage of their textbook:

• “I’ll never use this information.”
• “I can’t follow the explanations.”
I’ve written every page of the Sixth Edition with the intent of eliminating these two objections. The ideas and tools I’ve used to do so are described for the student in “A Brief Guide to Getting the Most from This Book,” which appears at the front of the book. How Does Precalculus Differ fromAlgebra and Trigonometry?

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 reªects those differences. Here are a few examples:

• Algebra and Trigonometry devotes an entire chapter to linear equations, rational equations, quadratic equations, radical equations, linear inequalities, and developing models involving these equations and inequalities. Precalculus reviews these topics in three sections of the prerequisites chapter (P.7: Equations; P.8: Modeling with Equations; P.9: Linear Inequalities and Absolute Value Inequalities). Functions, the core of any precalculus course, are then introduced in Chapter 1.

• Precalculus contains a section on constructing functions from verbal descriptions and formulas (1.10: Modeling with Functions) that is not included in Algebra and Trigonometry. Modeling skills are applied to situations that students are likely to see in calculus when solving applied problems involving maximum or minimum values.

• Precalculus develops trigonometry from the perspective of the unit circle (4.2: Trigonometric Functions: The Unit Circle). In Algebra and Trigonometry, trigonometry is developed using right triangles.

• Precalculus contains a chapter (Chapter 11: Introduction to Calculus) that takes the student into calculus with discussions of limits, continuity, and derivatives. This chapter is not included in Algebra and Trigonometry.

• Many of the liberal arts applications in Algebra and Trigonometry are replaced by more scienti c or higher level applications in Precalculus. Some examples:

• Black Holes in Space (P.2: Exponents and Scientific Notation)
• Average Velocity (1.5: More on Slope)
• Newton’s Law of Cooling (3.5: Exponential Growth and Decay; Modeling Data)

What’s New in the Sixth Edition?

• New Applications and Real-World Data. The Sixth Edition contains 63 worked-out examples and exercises based on new data sets, and 36 examples and exercises based on data updated from the Fifth Edition. Many of the new applications involve topics relevant to college students, including student-loan debt (Chapter–P, Mid-Chapter Check–Point, Exercise–42), grade inªation (Exercise Set P.7, Exercises–137–138), median earnings,–by  nal degree earned (Exercise Set–P.8, Exercises–3–4), excuses for not meeting deadlines (Chapter P Summary, Exercise 141), political orientation of college freshmen (Chapter 1 Summary, Exercise–67), sleep hours of college students (Exercise–Set 7.1, Exercise–86), and the number of hours college students study per week, by major (Exercise Set 7.2, Exercises–33–34).

• Brief Reviews. Beginning with Chapter 1, the Brief Review boxes that appear throughout the book summarize mathematical skills, many of which are course prerequisites, that students have learned, but which many students need to review. This feature appears whenever a particular skill is  rst needed and eliminates the need for you to reteach that skill. For more detail, students are referred to the appropriate section and objective in a previous chapter–where the topic is fully developed.

• Achieving Success. The Achieving Success boxes, appearing at the end of many sections in Chapters P through 6, offer strategies for persistence and success in college mathematics courses.

• Retaining the Concepts. Beginning with Chapter 1, Section 1.2, each Exercise Set contains three or four review exercises under the header “Retaining the Concepts.” These exercises are intended for students to review previously covered objectives in order to improve their understanding of the topics and to help maintain their mastery of the material. If students are not certain how to solve a review exercise, they can turn to the section and worked example given in parentheses at the end of each exercise. The Sixth Edition contains 216 new exercises in the “Retaining the Concepts” category.

• New Blitzer Bonus Videos with Assessment. Many of the Blitzer Bonus features throughout the textbook have been turned into animated videos that are built into the MyMathLab course. These videos help students make visual connections to algebra and trigonometry and the world around them. Assignable exercises have been created within the MyMathLab course to assess conceptual understanding and mastery. These videos and exercises can be turned into a media assignment within the Blitzer MyMathLab course.

• Updated Learning Guide. Organized by the textbook’s learning objectives, this updated Learning Guide helps students make the most of their textbook for test preparation. Projects are now included to give students an opportunity to discover and reinforce the concepts in an active learning environment and are ideal for group work in class.

• Updated Graphing Calculator Screens. All screens have been updated using the TI-84 Plus C.