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PRECALCULUS: REAL MATHEMATICS, REAL PEOPLE, Alternate Edition, 6th Edition, is an ideal student and instructor resource for courses that require the use of a graphing calculator. The quality and quantity of the exercises, combined with interesting applications and innovative resources, make teaching easier and help students succeed. Retaining the series' emphasis on student support, selected examples throughout the text include notations directing students to previous sections to review concepts and skills needed to master the material at hand. The book also achieves accessibility through careful writing and design--including examples with detailed solutions that begin and end on the same page, which maximizes readability. Similarly, side-by-side solutions show algebraic, graphical, and numerical representations of the mathematics and support a variety of learning styles. Reflecting its new subtitle, this significant revision focuses more than ever on showing students the relevance of mathematics in their lives and future careers.
- With the extensive revision to create the Sixth Edition, this book's original subtitle, "A Graphing Approach," no longer represents the text's essence (although the graphing calculator is still required). The author's changes and the new title, "PRECALCULUS: REAL MATHEMATICS, REAL PEOPLE," address a primary need in education today--relevance. The mathematics in this text is both real and relevant, and the people introduced are either already in or preparing for careers in which they will use mathematics.
- To facilitate familiarity with the basic functions, the book retains its compilation of several elementary and nonelementary functions in a Library of Parent Functions. As in the previous edition, each function is introduced at the first point of use in the text with a definition and description of basic characteristics. New to this edition are Library of Parent Functions Examples, which are identified in the title of the example, and the Review of Library of Parent Functions after Chapter 4. A summary of the functions appears on the inside cover of the text.
- As in previous editions, many examples present side-by-side solutions with multiple approaches––algebraic, graphical, and numerical. Often, the algebraic solution is formal, with step-by-step work. In the new edition, the graphical solutions have been revised to be more visual, providing a quick way for students to check the reasonableness of the solution obtained algebraically.
- The exercise sets have been carefully and extensively examined to ensure they are rigorous, relevant, and cover all topics suggested by our users. Many new skill building and challenging exercises have been added.
- Revised Chapter Summaries now include explanations and examples of the objectives taught in the chapter.
- For the past several years, we have maintained an independent website--CalcChat.com--that provides free solutions to all odd-numbered exercises in the text. Thousands of students using our textbooks have visited the site for practice and help with their homework. For the Sixth Edition, the information from CalcChat.com, including which solutions students accessed most often, was used to help guide the revision of the exercises.
- New Chapter Openers highlight real modeling data problems, each showing a graph of the data, a section reference, and a short description of the data.
- A new Explore the Concept feature engages students in active discovery of mathematical concepts, strengthens critical thinking skills, and helps build intuition.
- A new What's Wrong? feature points out common errors made using graphing utilities.
- A new Vocabulary and Concept Check appears at the beginning of the exercise set for each section. Each of these checks asks fill-in-the-blank, matching, and non-computational questions designed to help students learn mathematical terminology and to test basic understanding of that section's concepts.
- The section exercises are now grouped into four categories: Vocabulary and Concept Check, Procedures and Problem Solving, Conclusions, and Cumulative Mixed Review. Many of the exercises are titled for easy reference.
- New Algebraic-Graphical-Numerical Exercises allow students to solve a problem using multiple approaches. This helps students see that a problem can be solved in more than one way--and that different methods yield the same result.
- New Modeling Data Exercises are multi-part applications that involve real-life data, offering students the opportunity to generate and analyze mathematical models.
- New Capstone Exercises, one per section, are conceptual problems that synthesize key topics and provide students with a better understanding of the concepts in a section. These exercise are excellent for classroom discussion or test preparation.
- Progressive Summaries after every three chapters outline newly introduced topics and contextualize them within the framework of the course.
- Make a Decision exercises--extended modeling applications presented at the end of selected exercise sets--give students the opportunity to apply the mathematical concepts and techniques they've learned to large sets of real data.
- The Library of Functions, threaded throughout the text, defines each elementary function and its characteristics at first point of use. Exercises test students' understanding of these functions. All elementary functions are also presented in a summary on the front endpapers of the text for convenient reference.
- Chapter Summaries include the key terms and key concepts that are covered in the chapter, serving as an effective study aid by providing a single point of reference for review.
- The Proofs of Selected Theorems are presented at the end of each chapter for easy reference.
- Technology Tips point out the pros and cons of technology use in certain mathematical situations, and provide alternative methods of solving or checking a problem using a graphing calculator.
- Students may sometimes be misled by the visuals generated by graphing calculators, so the authors use color to enhance the graphing calculator displays in the textbook, where appropriate. This enables students to visualize concepts accurately and efficiently.
- Technology Support notes throughout the text refer students to the Technology Support Guide Appendix A, where they can learn how to use specific graphing calculator features to enhance their understanding of the concepts presented. The Technology Support notes also direct students to the Graphing Technology Guide, accessible on the textbook's website, for keystroke support for numerous calculator models.
- Carefully positioned throughout the text, Explorations engage students in active discovery of mathematical concepts, strengthening critical thinking skills and helping them to develop an intuitive understanding of theoretical concepts.
- What You Should Learn and Why You Should Learn It appears at the beginning of each chapter and section, offering students a succinct list of the concepts they will soon encounter. Additionally, this feature refers students to an application in the exercise set which helps put the math concept into a real-life context so students can understand it better.
- To help prepare students who intend to move on to Calculus, the authors have placed an icon next to algebraic techniques that are used in Calculus.
Real Numbers. Exponents and Radicals. Polynomials and Factoring. Rational Expressions. The Cartesian Plane. Representing Data Graphically.
1. FUNCTIONS AND THEIR GRAPHS.
Introduction to Library of Functions. Graphs of Equations. Lines in the Plane. Functions. Graphs of Functions. Shifting, Reflecting, and Stretching Graphs. Combinations of Functions. Inverse Functions.
2. SOLVING EQUATIONS AND INEQUALITIES.
Linear Equations and Problem Solving. Solving Equations Graphically. Complex Numbers. Solving Quadratic Equations Algebraically. Solving Other Types of Equations Algebraically. Solving Inequalities Algebraically and Graphically. Linear Models and Scatter Plots. Cumulative Test: Chapters P–2. Progressive Summary: Chapters P–2.
3. POLYNOMIAL AND RATIONAL FUNCTIONS.
Quadratic Functions. Polynomial Functions of Higher Degree. Real Zeros of Polynomial Functions. The Fundamental Theorem of Algebra. Rational Functions and Asymptotes. Graphs of Rational Functions. Quadratic Models. Cumulative Test: Chapters 1-3.
4. EXPONENTIAL AND LOGARITHMIC FUNCTIONS.
Exponential Functions and Their Graphs. Logarithmic Functions and Their Graphs. Properties of Logarithms. Solving Exponential and Logarithmic Equations. Exponential and Logarithmic Models. Nonlinear Models. Cumulative Test: Chapters 3–4. Progressive Summary: Chapters P–4.
5. TRIGONOMETRIC FUNCTIONS.
Angles and Their Measure. Right Triangle Trigonometry. Trigonometric Functions of Any Angle. Graphs of Sine and Cosine Functions. Graphs of Other Trigonometric Functions. Inverse Trigonometric Functions. Applications and Models. Library of Parent Functions Review.
6. ANALYTIC TRIGONOMETRY.
Using Fundamental Identities. Verifying Trigonometric Identities. Solving Trigonometric Equations. Sum and Difference Formulas. Multiple-Angle and Product-to-Sum Formulas.
7. ADDITIONAL TOPICS IN TRIGONOMETRY.
Law of Sines. Law of Cosines. Vectors in the Plane. Vectors and Dot Products. Trigonometric Form of a Complex Number. Cumulative Test: Chapters 5–7.
Progressive Summary: Chapters P–7.
8. LINEAR SYSTEMS AND MATRICES.
Solving Systems of Equations. Systems of Linear Equations in Two Variables. Multivariable Linear Systems. Matrices and Systems of Equations. Operations with Matrices. The Inverse of a Square Matrix. The Determinant of a Square Matrix. Applications of Matrices and Determinants.
9. SEQUENCES, SERIES, AND PROBABILITY.
Sequences and Series. Arithmetic Sequences and Partial Sums. Geometric Sequences and Series. The Binomial Theorem. Counting Principles. Probability.
10. TOPICS IN ANALYTIC GEOMETRY.
Circles and Parabolas. Ellipses. Hyperbolas. Parametric Equations. Polar Coordinates. Graphs of Polar Equations. Polar Equations of Conics. Cumulative Test: Chapters 8–10.
Progressive Summary: Ch P–10.
APPENDIX A: TECHNOLOGY SUPPORT GUIDE.
APPENDIX B: CONCEPTS IN STATISTICS (Web only).
Measures of Central Tendency and Dispersion. Least Squares Regression.
APPENDIX C: VARIATION (Web only)
APPENDIX D: SOLVING LINEAR EQUATIONS AND INEQUALITIES (Web only).
APPENDIX E: SYSTEMS OF INEQUALITIES (Web only).
Solving Systems of Inequalities. Linear Programming.
APPENDIX F: MATHEMATICAL INDUCTION (Web only).
PowerLecture with ExamView®
This CD-ROM (or DVD) provides the instructor with dynamic media tools for teaching. Create, deliver, and customize tests (both print and online) in minutes with ExamView® Computerized Testing Featuring Algorithmic Equations. Easily build solution sets for homework or exams using Solution Builder's online solutions manual. Microsoft® PowerPoint® lecture slides and figures from the book are also included on this CD-ROM (or DVD).
These text-specific DVDs cover all sections of the text and provide explanations of key concepts, examples, exercises, and applications in a lecture-based format.