Description

For courses in college algebra and trigonometry .

Steadfast Support for your Evolving Course

The College Algebra series, by Lial, Hornsby, Schneider, and Daniels, combines the experience of master teachers to help students develop both the conceptual understanding and the analytical skills necessary for success in mathematics. With this latest edition, the authors respond to the challenges of new student expectations and new classroom models.

MyMathLab not included. Students, if MyMathLab is a recommended/mandatory component of the course, please ask your instructor for the correct ISBN and course ID. MyMathLab should only be purchased when required by an instructor. Instructors, contact your Pearson representative for more information.

Also available with MyMathLab

MyMathLab is an online homework, tutorial, and assessment program designed to work with this text to engage students and improve results. Within its structured environment, students practice what they learn, test their understanding, and pursue a personalized study plan that helps them absorb course material and understand difficult concepts.

The authors have developed specific content in MyMathLab to give students the practice they need to develop a conceptual understanding of College Algebra and the analytical skills necessary for success in mathematics. The MyMathLab features support College Algebra students in a variety of classroom formats (traditional, hybrid, and online).

Features

This title is a Pearson Global Edition. The Editorial team at Pearson has worked closely with educators around the world to include content which is especially relevant to students outside the United States.

About the Book

Support for Learning Concepts: a systematic approach is used to present each topic, and is designed to actively engage students in the learning process. As a result, students develop both the conceptual understanding and the analytical skills necessary for success.

• NEW! Concept Preview Exercises now begin each homework section to ensure students’ understanding of vocabulary and basic concepts, especially for hybrid, online, and flipped courses. These are also assignable in MyMathLab and also available in Learning Catalytics.
• Pointers in the examples provide on-the-spot reminders and warnings about common pitfalls. Examples now offer additional side comments where appropriate in the step-by-step solutions, and there are more section references to previously covered material.
• Now Try exercises conclude every example with a reference to one or more parallel, odd-numbered exercises from the corresponding exercise set. Students are able to immediately apply and reinforce the concepts and skills presented in the examples, while actively engaging in the learning process.

• Real-life applications in the examples and exercises draw from fields such as business, pop-culture, sports, life sciences, and environmental studies to show the relevance of algebra to daily life.
• Functions are introduced in Chapter 2 and are a unifying theme throughout the text.
  • Function boxes offer a comprehensive, visual introduction to each class of function and also serve as an excellent resource for student reference and review throughout the course. Each function box includes a table of values alongside traditional and calculator graphs, as well as the domain, range, and other specific information about the function.
  • Animations are available within MyMathLab.
• Graphing calculator coverage is optional and may be omitted without loss of continuity. The authors stress that these devices can be useful as an aid to understanding, but that students must master the underlying mathematical concepts first.
  • Graphing calculator solutions are included for selected examples, as appropriate.
  • Graphing calculator notes and exercises are marked with an icon for easy identification and flexibility.
• Cautions and Notes boxes throughout the text give students warnings of common errors and emphasize important ideas.
• Looking Ahead to Calculus offers glimpses of how the algebraic topics currently being studied are used in calculus. These notes can be found in the margins of the text in key places.
• Connections boxes provide connections to the real world or to other mathematical concepts, historical backgrounds, and thought-provoking questions for writing, class discussion, or group work.
• Chapter Openers provide a motivating application topic that is tied to the chapter content, plus a list of sections and any quizzes or summary exercises in the chapter.

Support for Practicing Concepts: the variety of exercise types promotes understanding of the concepts and reduces the opportunity for rote memorization.

• Nearly 1,000 of the exercises are new or modified in this edition.
• Quizzes allow students to periodically check their understanding of the material covered. At least one quiz now appears in each chapter, where appropriate.
• Connecting Graphs with Equations problems, by request, provide students with opportunities to write equations for given graphs.
• Concept Check exercises focus on mathematical thinking and conceptual understanding.
• Relating Concepts Exercises help students tie together topics and develop problem-solving skills as they compare and contrast ideas, identify and describe patterns, and extend concepts to new situations. These exercises make great collaborative activities for pairs or small groups of students and are available in selected exercise sets. These are also assignable in MyMathLab.
• Summary Exercises are mixed review problems that challenge students to reconcile recent topics learned, synthesize concepts, and select appropriate solution methods.
• Standard exercise types include writing exercises, optional graphing calculator exercises, multiple-choice, matching, true/false, and completion problems.

Support for Review and Test Preparation: ample opportunities for review are interspersed within chapters and also found at the end of chapters.

• Quizzes appear periodically throughout the chapter for students to check their progress. Answers are located in the student answer section at the back of the text.
• Mid-chapter quizzes are assignable in MyMathLab.
• Summary Exercises offer mixed review, requiring students to decide which methods covered in the chapter should apply to a particular problem.
• Cumulative Review assignments are available to assign in MyMathLab for each chapter.
• Chapter Reviews and Test Prep conclude every chapter with the following features:
  • An extensive Summary, featuring a section-by-section list of Key Terms and New Symbols.
  • A Quick Review of important concepts, presented alongside corresponding Examples. Also presented in video format and assignable in MyMathLab.
  • A comprehensive set of Review Exercises.
  • A Chapter Test covering all skills and concepts from the chapter.

MyMathLab not included. Students, if MyMathLab is a recommended/mandatory component of the course, please ask your instructor for the correct ISBN and course ID. MyMathLab should only be purchased when required by an instructor. Instructors, contact your Pearson representative for more information.

Also available with MyMathLab

MyMathLab^® is an online homework, tutorial, and assessment program designed to work with this text to engage students and improve results. Within its structured environment, students practice what they learn, test their understanding, and pursue a personalized study plan that helps them absorb course material and understand difficult concepts.

The authors have developed specific content in MyMathLab to give students the practice they need to develop a conceptual understanding of College Algebra and the analytical skills necessary for success in mathematics. The MyMathLab features described here support College Algebra students in a variety of classroom formats (traditional, hybrid and online).

• Example Solution videos present the detailed solution process for every example in the text.
• Quick Reviews cover definitions and procedures for each section.
• MyNotes provide a note-taking structure for students to use while they read the textbook or watch the MyMathLab videos.
• MyClassroomExamples offer structure for notes taken during lecture, and are for use with the Classroom Examples.
• Both MyNotes and MyClassroomExamples are available in MyMathLab and can be customized by the instructor.

Support for All Classroom Types: a complete suite of instructional materials makes it easier for instructors to prepare for the course, and leads to greater student success. Updates to MyMathLab^® and MathXL^® are an integral part of supporting instructor and student success in today’s classroom.

• MyNotes, from co-author Callie Daniels, provide structure for student note taking.
• NEW! Guided Visualizations bring mathematical concepts to life. These animated figures help students visualize the concepts through directed explorations and purposeful manipulation. Guided Visualizations are assignable in MyMathLab and encourage active learning, critical thinking, and conceptual learning.
• The video program is designed to help students study anytime, anywhere.
  • Quick Reviews cover key definitions and procedures from each section.
  • Example Solutions walk students through the detailed solution process for every example in the textbook.
• Additional MathXL quizzes are assignable as homework. These are based on the text’s mid-chapter quizzes.
• Cumulative assignments follow each chapter test in the homework and test manager, allowing students to synthesize previous material throughout the course. These assignments consist of 30 problems each.

New to this Edition

New and Updated Features

• NEW! Concept Preview Exercises now begin each homework section to ensure students’ understanding of vocabulary and basic concepts, especially for hybrid, online, and flipped courses. These are also assignable in MyMathLab and also available in Learning Catalytics.
• Nearly 1,000 of the exercises are new or modified in this edition.

MyMathLab not included. Students, if MyMathLab is a recommended/mandatory component of the course, please ask your instructor for the correct ISBN and course ID. MyMathLab should only be purchased when required by an instructor. Instructors, contact your Pearson representative for more information.

Also available with MyMathLab

MyMathLab^® is an online homework, tutorial, and assessment program designed to work with this text to engage students and improve results. Within its structured environment, students practice what they learn, test their understanding, and pursue a personalized study plan that helps them absorb course material and understand difficult concepts.

The authors have developed specific content in MyMathLab to give students the practice they need to develop a conceptual understanding of College Algebra and the analytical skills necessary for success in mathematics. The MyMathLab features described here support College Algebra students in a variety of classroom formats (traditional, hybrid and online).

• NEW! Concept Preview Exercises now begin each homework section to ensure students’ understanding of vocabulary and basic concepts, especially for hybrid, online, and flipped courses. These are assignable in MyMathLab and also available in Learning Catalytics.
• NEW! Guided Visualizations bring mathematical concepts to life. These animated figures help students visualize the concepts through directed explorations and purposeful manipulation. Guided Visualizations are assignable in MyMathLab and encourage active learning, critical thinking, and conceptual learning.

Table of Contents

R. Review of Basic Concepts

R-1 Sets

R-2 Real Numbers and Their Properties

R-3 Polynomials

R-4 Factoring Polynomials

R-5 Rational Expressions

R-6 Rational Exponents

R-7 Radical Expressions

1. Equations and Inequalities

1-1 Linear Equations

1-2 Applications and Modeling with Linear Equations

1-3 Complex Numbers

1-4 Quadratic Equations

1-5 Applications and Modeling with Quadratic Equations

1-6 Other Types of Equations and Applications

1-7 Inequalities

1-8 Absolute Value Equations and Inequalities

2. Graphs and Functions

2-1 Rectangular Coordinates and Graphs

2-2 Circles

2-3 Functions

2-4 Linear Functions

2-5 Equations of Lines and Linear Models

2-6 Graphs of Basic Functions

2-7 Graphing Techniques

2-8 Function Operations and Composition

3. Polynomial and Rational Functions

3-1 Quadratic Functions and Models

3-2 Synthetic Division

3-3 Zeros of Polynomial Functions

3-4 Polynomial Functions: Graphs, Applications, and Models

3-5 Rational Functions: Graphs, Applications, and Models

3-6 Variation

4. Inverse, Exponential, and Logarithmic Functions

4-1 Inverse Functions

4-2 Exponential Functions

4-3 Logarithmic Functions

4-4 Evaluating Logarithms and the Change-of-Base Theorem

4-5 Exponential and Logarithmic Equations

4-6 Applications of Models of Exponential Growth and Decay

5. Trigonometric Functions

5-1 Angles

5-2 Trigonometric Functions

5-3 Trigonometric Function Values and Angle Measures

5-4 Solutions and Applications of Right Triangles

6. The Circular Functions and Their Graphs

6-1 Radian Measure

6-2 The Unit Circle and Circular Functions

6-3 Graphs of the Sine and Cosine Functions

6-4 Translations of the Graphs of the Sine and Cosine Functions

6-5 Graphs of the Tangent and Cotangent Functions

6-6 Graphs of the Secant and Cosecant Functions

6-7 Harmonic Motion

7. Trigonometric Identities and Equations

7-1 Fundamental Identities

7-2 Verifying Trigonometric Identities

7-3 Sum and Difference Identities

7-4 Double-Angle and Half-Angle Identities

7-5 Inverse Circular Functions

7-6 Trigonometric Equations

7-7 Equations Involving Inverse Trigonometric Functions

8. Applications of Trigonometry

8-1 The Law of Sines

8-2 The Law of Cosines

8-3 Geometrically Defined Vectors and Applications

8-4 Algebraically Defined Vectors and the Dot Product

8-5 Trigonometric (Polar) Form of Complex Numbers; Products and Quotients

8-6 De Moivre’s Theorem; Powers and Roots of Complex Numbers

8-7 Polar Equations and Graphs

8-8 Parametric Equations, Graphs, and Applications

9. Systems and Matrices

9-1 Systems of Linear Equations

9-2 Matrix Solution of Linear Systems

9-3 Determinant Solution of Linear Systems

9-4 Partial Fractions

9-5 Nonlinear Systems of Equations

9-6 Systems of Inequalities and Linear Programming

9-7 Properties of Matrices

9-8 Matrix Inverses

10. Analytic Geometry

10-1 Parabolas

10-2 Ellipses

10-3 Hyperbolas

10-4 Summary of the Conic Sections

11. Further Topics in Algebra

11-1 Sequences and Series

11-2 Arithmetic Sequences and Series

11-3 Geometric Sequences and Series

11-4 The Binomial Theorem

11-5 Mathematical Induction

11-6 Counting Theory

11-7 Basics of Probability

Appendices