# Precalculus Essentials, 1st edition

Published by Pearson (January 22, 2013) © 2014

**J S Ratti**University of South Florida**Marcus S. McWaters**University of South Florida**Leslaw Skrzypek**University Of South Florida

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**Ratti** and **McWaters** wrote this series with the primary goal of preparing students to be successful in calculus. Having taught both calculus and precalculus, the authors saw firsthand where students would struggle, where they needed help making connections, and what material they needed in order to succeed in calculus. Their experience in the classroom shows in each chapter, where they emphasize conceptual development, real-life applications, and extensive exercises to encourage a deeper understanding.

**Precalculus Essentials**, this text offers the best of both worlds: fast-paced, rigorous topics and a friendly, “teacherly” tone. This text is developed with a focus on key topics for calculus preparation.

**Precalculus Essentials** offers a fast pace and includes more rigorous topics ideal for students heading into calculus. More than just a truncated version of a longer book, the table of contents is condensed, combined, and learning-objectives-based, especially designed for a one-quarter/one-semester course.

**A faster pace**gets right into functions in Chapter 1, with a review of algebra in Chapter P.**Trigonometric functions**are introduced in Chapter 4 with a unit circle approach, before developing the right triangle.**Right triangle applications**(height and distance) are covered in Chapter 5, Applications of Trigonometric Functions.**Maintaining Skills**problems appear in every section’s exercise set, providing ongoing review of skills frequently required in Calculus courses.**Exercises for Calculus**appear in every end-of-chapter exercise set, ensuring students can be well prepared for the calculus courses in their future.

**Features of the Ratti/McWaters series:**

**Student-friendly support**features in Ratti/McWaters are designed to help students to see not only what they are going to learn, but also why, so that every concept is given the proper context.**Topics for review**help students refresh their memories on essential topics before beginning each chapter, listing specific page references to make it easy to find those concepts.- Clear
**Objectives**preview the key points of the section ahead, providing easy reference points when studying for exams. These**Objectives**appear again at the appropriate places in the section, putting each new topic into context. **Every section**opens with an engaging**Application**that is revisited later in the section through examples and exercises. The Application ties key ideas together and provides motivation for students to read and study.**Work it out:**As you would in your own class, Ratti and McWaters encourage students to practice the material frequently, and give them ample opportunities to master the material by solving problems and applying their understanding.**Procedure in Action**is a special feature which introduces procedure steps within the context of a worked-out example. Important multistep procedures, such as the steps for finding the inverse of a one-to-one function, are presented in a two-column format. The numbered steps of the procedure are given in the left column, and an example is worked out step-by-step, aligned with and numbered as the procedure steps, in the right column. This approach provides students with a clear solution model when encountering difficulty in their work.- All examples conclude with a
**Practice Problem**to ensure that students grasp the concept before moving forward. **Exercises**are plentiful and each section ends with three levels of exercises for students to practice the math and apply their understanding:**Basic Concepts and Skills**are suitable for all students and homework assignments. Now included are new fill-in-the-blank and true/false exercises that test whether basic concepts and vocabulary of the section have been absorbed.**Maintaining Skills**exercises refresh concepts learned in previous chapters and allow for practice of skills needed in the upcoming chapter**Applying the Concepts**are perfect for all students and homework assignments.- Additional exercise typesinclude
**Critical Thinking/Discussion/Writing**and graphing calculator exercises. **Help along the way:**These integrated study aids give students hints and tips at strategic places in the text, addressing some of the most frequent issues and questions that occur in office hours.**Recall**notes, located in the margins, periodically remind students of a key idea they learned earlier in the text that will help them with the new problem at hand.**Warning**notes point out commonly-made errors in thinking and calculations, with specific examples and detailed guidance.**Side Notes**offer just-in-time hints on essential skills.**Do You Know?**marginal notes keeps students engaged with interesting facts and information.**Historical Notes**cover key people and ideas in the history and development of mathematics.**Technology Connections**, although optional, give students tips on using their calculators to check answers and reinforce concepts.**Preparation and review—**end-of-chapter material includes all of the following items to help students prepare for exams and make the most of their study time.**Summary of Definitions, Concepts, and Formulas**lists key ideas from the chapter for convenient review.**Review Exercises**cover all concepts from the chapter.**Exercises for Calculus**allow students to practice skills that will be useful in their future calculus courses.**Two full Practice Tests**, one multiple-choice and one open-ended, help students prepare for any exam format.**MyMathLab**anticipates the needs of today’s students and academic environment. MyMathLab enhancements not only engage students, but make them think more visually, critically, and conceptually.**Getting Ready**material includesquick quizzes and personalized just-in-time review integrated throughout the course as needed, to prepare students with prerequisite material to succeed. From these quizzes, a personalized just-in-time review assignment is generated for each student, allowing them to refresh forgotten concepts.**Interactive Figures**are now available, enabling users to manipulate figures to bring hard-to-convey math concepts to life.**Icons**throughout the etext in MyMathLab direct students to an Interactive Figure to bring the concept to life.. Interactive figures are also assignable in MyMathLab and Exploratory Exercises are available in Instructor Resources.**Enhanced Graphing Utility**allows students to graph3-point quadratic, 4-point cubic, and transformation graphs (which include sine, cosine, logarithmic, and exponential functions). These new graphing questions are assignable in MyMathLab. These are also assignable in MyMathLab.**Video Assessment**is assignable exercises that are tied to example videos and are now available to help students retain valuable information presented in the videos.**Two MyMathLab course options**are now available: a standard course and a Ready to Go course.**Standard MyMathLab**courses allow instructors to build their course their way, offering maximum flexibility and complete control over all aspects of assignment creation.- The new
**Ready to Go**courses provide students with all the same great MyMathLab features, but make it easier for instructors to get started. Each course includes pre-assigned homework and quizzes to make creating a course even easier.

**P. Basic Concepts of Algebra**

P.1 The Real Numbers; Integer Exponents

P.2 Radicals and Rational Exponents

P.3 Solving Equations

P.4 Inequalities

P.5 Complex Numbers

**1. Graphs and Functions**

1.1 Graphs of Equations

1.2 Lines

1.3 Functions

1.4 A Library of Functions

1.5 Transformations of Functions

1.6 Combining Functions; Composite Functions

1.7 Inverse Functions

Chapter 1 Summary

Chapter 1 Review Exercises

Chapter 1 Exercises for Calculus

Chapter 1 Practice Test A

Chapter 1 Practice Test B

**2. Polynomial and Rational Functions**

2.1 Quadratic Functions

2.2 Polynomial Functions

2.3 Dividing Polynomials and the Rational Zeros Test

2.4 Zeros of a Polynomial Function

2.5 Rational Functions

Chapter 2 Summary

Chapter 2 Review Exercises

Chapter 2 Exercises for Calculus

Chapter 2 Practice Test A

Chapter 2 Practice Test B

**3. Exponential and Logarithmic Functions**

3.1 Exponential Functions

3.2 Logarithmic Functions

3.3 Rules of Logarithms

3.4 Exponential and Logarithmic Equations and Inequalities

Chapter 3 Summary

Chapter 3 Review Exercises

Chapter 3 Exercises for Calculus

Chapter 3 Practice Test A

Chapter 3 Practice Test B

**4. Trigonometric Functions**

4.1 Angles and Their Measure

4.2 The Unit Circle; Trigonometric Functions

4.3 Graphs of the Sine and Cosine Functions

4.4 Graphs of the Other Trigonometric Functions

4.5 Inverse Trigonometric Functions

4.6 Right-Triangle Trigonometry

4.7 Trigonometric Identities

4.8 Sum and Difference Formulas

Chapter 4 Summary

Chapter 4 Review Exercises

Chapter 4 Exercises for Calculus

Chapter 4 Practice Test A

Chapter 4 Practice Test B

**5. Applications of Trigonometric Functions**

5.1 The Law of Sines and the Law of Cosines

5.2 Areas of Polygons Using Trigonometry

5.3 Polar Coordinates

5.4 Parametric Equations

Chapter 5 Summary

Chapter 5 Review Exercises

Chapter 5 Exercises for Calculus

Chapter 5 Practice Test A

Chapter 5 Practice Test B

**6. Further Topics in Algebra**

6.1 Sequences and Series

6.2 Arithmetic Sequences; Partial Sums

6.3 Geometric Sequences and Series

6.4 Systems of Equations in Two Variables

6.5 Partial-Fraction Decomposition

Chapter 6 Summary

Chapter 6 Review Exercises

Chapter 6 Exercises for Calculus

Chapter 6 Practice Test A

Chapter 6 Practice Test B

Appendix: Answers to Practice Problems

**J.S.Ratti **has been teaching mathematics at all levels for over 35 years. He is currently a full professor of mathematics and director of the Center for Mathematical Services at the University of South Florida. Professor Ratti is the author of numerous research papers in analysis, graph theory, and probability. He has won several awards for excellence in undergraduate teaching at University of South Florida and is known as the coauthor of a successful finite mathematics textbook.

**Marcus McWaters**is currently the chair of the Mathematics Department at the University of South Florida, a position he has held for the last eleven years. Since receiving his PhD in mathematics from the University of Florida, he has taught all levels of undergraduate and graduate courses, with class sizes ranging from 3 to 250. As chair, he has worked intensively to structure a course delivery system for lower level courses that would improve the low retention rate these courses experience across the country. When not involved with mathematics or administrative activity, he enjoys playing racquetball, spending time with his two daughters, and traveling the world with his wife.

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