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PRECALCULUS prepares students for calculus and the rigors of that course, having been written by teachers who have taught the courses and seen where students need help--and where other texts have come up short. The text features precise definitions and exposition, carefully crafted pedagogy, and a strong emphasis on algebraic, transcendental, and trigonometric functions. To show students how important and relevant precalculus topics are to their future coursework, an optional Looking Ahead to Calculus feature appears in each chapter. The varied examples and exercises include many that encourage students to use and understand graphs, as opposed to simply draw them, providing additional sound preparation for calculus.
- LOOKING AHEAD TO CALCULUS: Offering an interesting glimpse into calculus, this feature demonstrates the relevance of precalculus topics to students' future success. Each feature (placed at the end of the chapter to allow instructional flexibility) includes objectives referencing the related chapter material, discussion of the topics, and "Connect to Calculus" exercises. References to this optional material (highlighted so that instructors may teach or skip it at their discretion) appear throughout each chapter, reinforcing the connection between the topics at hand and future courses.
- TITLED EXAMPLES: Descriptive titles have been added to clearly identify the topic and purpose of each example.
- EXAMPLE STRUCTURE: To help students gain a deeper understanding of how to solve each problem, solutions begin with a stated approach. The examples are engaging and step-by-step solutions with annotations are provided.
- SELF CHECKS: Each example is followed immediately by a Self Check exercise that actively reinforces student understanding of concepts and example solutions. The answers for students are offered at the end of each section. To assist instructors, the answers appear next to the problem in the Annotated Instructor's Edition, printed in blue.
- NOW TRY EXERCISES: A reference to a Now Try exercise follows all Examples and Self Check problems, providing students an additional opportunity to assess their understanding of the concept related to each worked example. These references also show students a correspondence between the examples in the book and the exercise sets.
- APPLICATION EXAMPLES: Applications from a wide range of disciplines demonstrate how mathematics is used to solve real problems, answering the student question, "When will I ever use this math?" These applications, many accompanied by an eye-catching photo, motivate the material and help students become better problem solvers.
- GETTING READY EXERCISES: Each problem set begins with Getting Ready exercises, which test students' understanding of concepts and proper use of mathematical vocabulary. Students should be able to answer these fill-in-the blank questions before moving on to the Practice exercises.
- COMPREHENSIVE EXERCISE SETS: To improve mathematical skills and cement understanding, the exercise sets progress from routine to more challenging. The mathematics in each exercise set is sound, but not so rigorous that it will confuse students. All exercise sets include Getting Ready, Practice, Application, and Discovery and Writing problems.
- INTERESTING AND CONTEMPORARY APPLICATION EXERCISES: Application exercises, all with titles, reflect the book's emphasis on solving problems through realistic applications,
- CHAPTER REVIEWS AND CHAPTER TESTS: Each chapter closes with a Chapter Review and Chapter Test, giving students the best opportunity for study and exam preparation. Chapter Reviews are comprehensive and consist of three parts: definitions and concepts, examples, and review exercises. Chapter Tests cover all the important topics and yet are brief enough to emulate a "real-time" test, so students can practice not only the math but also their test-taking aptitude. As an additional quick reference, endpapers offer the important formulas and graphs developed in the book.
- ACCENTS ON TECHNOLOGY AND CALCULATORS: Accents on Technology appear throughout the textbook to encourage students to become intelligent users of technology and grasp concepts graphically. They illustrate and guide the use of a TI-84 graphing calculator for specific problems. Although graphing calculators are incorporated into the book, their use is not required. All graphing topics are fully discussed in traditional ways.
- CAREERS IN MATHEMATICS CHAPTER OPENERS: To encourage students to explore careers that use mathematics and make a connection between math and real life, each chapter opens with Careers in Mathematics. New, exciting careers are showcased in this edition. Featuring information taken primarily from the Occupational Outlook Handbook, these snapshots include information on how professionals use math in their work and who employs them. A web address is provided, allowing students to learn more about the career.
- SECTION OPENERS: Each section begins with a contemporary photo and a real-life application that will appeal to students of varied interests, piquing interest and motivating students to read the material.
- NUMBERED OBJECTIVES: Numbered learning objectives, which are listed at the beginning of each section and appear as subheadings in the section, keep students focused.
- STUDENT-FRIENDLY WRITING STYLE: Clear, concise, and friendly exposition helps to alleviate student anxiety about reading a mathematics textbook. The writing is informal yet accurate. Students and instructors alike should find the reading both interesting and inviting.
- STRATEGY BOXES: To enable students to build on their mathematical reasoning and approach problems with confidence, Strategy boxes offer problem-solving techniques and steps at appropriate points in the material.
- CAUTION BOXES: Caution boxes appear throughout the text to alert students to common errors and misunderstandings, and reinforce correct mathematics.
- COMMENTS: Comment boxes appear throughout the textbook, providing additional insights; for instance, clarification on a specific step or concept in an example, or a tip for studying the material.
Linear Equations and Applications. Complex Numbers. Quadratic Equations and Applications. Other Types of Equations. Inequalities. The Rectangular Coordinate System. Equations of Lines. Chapter Summary. Chapter Test. Looking Ahead to Calculus.
1. GRAPHS AND FUNCTIONS.
Graphs of Equations. Functions and Function Notation. Graphs of Functions. Basic Graphs. Transformations of Graphs. Operations on Functions. Inverse Functions. Chapter Summary. Chapter Test. Looking Ahead to Calculus.
2. POLYNOMIAL AND RATIONAL FUNCTIONS.
Quadratic Functions. Polynomial Functions. Rational Zeros of Polynomial Functions. Roots of Polynomial Equations. Rational Functions. Polynomial and Rational Inequalities. Chapter Summary. Chapter Test. Looking Ahead to Calculus.
3. EXPONENTIAL AND LOGARITHMIC FUNCTIONS.
Exponential Functions, Graphs, and Applications. Applications of Exponential Functions. Logarithmic Functions and Their Graphs. Applications of Logarithmic Functions. Properties of Logarithms. Exponential and Logarithmic Equations. Chapter Summary. Chapter Test. Looking Ahead to Calculus.
4. TRIGONOMETRIC FUNCTIONS.
Angles and Their Measurement. The Unit Circle and Trigonometric Functions. Trigonometric Functions of Any Angle; Fundamental Identities. Graphs of the Sine and Cosine Functions. Graphs of the Tangent, Cotangent, Secant and Cosecant Functions. Regression and Other Graphs Involving Trigonometric Functions. Chapter Summary. Chapter Test. Looking Ahead to Calculus.
5. ANALYTIC TRIGONOMETRY.
Inverse Trigonometric Functions. Inverse Cotangent, Secant, and Cosecant Functions (Optional). Verifying Trigonometric Identities. Sum and Difference Formulas. Double-Angle, Power-Reduction, Half-Angle Formulas. Product-to-Sum and Sum-to-Product Formulas. Trigonometric Equations I. Trigonometric Equations II. Chapter Summary. Chapter Test. Looking Ahead to Calculus.
6. APPLICATIONS; OBLIQUE TRIANGLES.
Solving Right Triangles. More Right Triangle Applications. Law of Sines. Law of Cosines. Area of Triangles. Angular and Linear Velocity--Circular Motion. Chapter Summary. Chapter Test. Looking Ahead to Calculus.
7. POLAR COORDINATES; VECTORS.
Polar Coordinates. Polar Equations and Graphs. Complex Plane; Polar Form of Complex Numbers; DeMoivre''s Theorem. Vectors. Dot Product. Chapter Summary. Chapter Test.
Looking Ahead to Calculus.
8. LINEAR SYSTEMS AND MATRICES.
Systems of Linear Equations. Gaussian Elimination and Matrix Methods. Matrix Algebra. Matrix Inversion. Determinants. Partial Fractions. Graphs of Linear Inequalities. Linear Programming (available on website). Chapter Summary. Chapter Test. Looking Ahead to Calculus.
9. CONIC SECTIONS AND QUADRATIC SYSTEMS.
The Circle and the Parabola. The Ellipse. The Hyperbola. Solving Non-linear Systems of Equations. Plane Curves and Parametric Equations. Conic Sections in Polar Coordinates. Chapter Summary. Chapter Test. Looking Ahead to Calculus.
10. NATURAL NUMBER FUNCTIONS AND PROBABILITY.
The Binomial Theorem. Sequences, Series, and Summation Notation. Arithmetic Sequences. Geometric Sequences. Mathematical Induction. Permutations and Combinations (available on website). Probability (available on website). Chapter Summary. Chapter Test. Looking Ahead to Calculus.
11. INTRODUCTION TO CALCULUS (available on website).
Limits. Properties of Limits. Limits and Continuity. Average Rate of Change. Tangents and Derivatives. Area and Integrals. Chapter Summary. Chapter Test.
Sets of Real Numbers. Integer Exponents and Scientific Notation. Radicals and Rational Exponents. Polynomials. Factoring Polynomials. Rational Expressions.
Cengage provides a range of supplements that are updated in coordination with the main title selection. For more information about these supplements, contact your Learning Consultant.
PowerLecture with ExamView®
This CD-ROM (or DVD) provides the instructor with dynamic media tools for teaching, including Microsoft® PowerPoint® lecture slides and figures from the book. 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 by using the link to Solution Builder's online solutions manual.
Text-Specific Videos on DVD
These text-specific instructional videos provide students with visual reinforcement of concepts and explanations, given in easy-to-understand terms with detailed examples and sample problems. A flexible format offers versatility for quickly accessing topics or catering lectures to self-paced, online, or hybrid courses. Closed captioning is provided for the hearing impaired.
Save time with this accurate Test Bank that offers multiple tests per chapter as well as final exams. The tests combine multiple-choice, free-response, and fill-in-the-blank questions for your convenience.
Student Solutions Manual
Contains fully worked-out solutions to all of the odd-numbered exercises in the text, giving students a way to check their answers and ensure that they took the correct steps to arrive at an answer.
Student Solutions Manual