Graphical Approach to Precalculus with Limits Pearson New International Edition, plus MyMathLab without eText

Series
Pearson
Author
John Hornsby / Margaret Lial / Gary K. Rockswold  
Publisher
Pearson
Cover
Softcover
Edition
5
Language
English
Pub.-date
October 2013
ISBN13
9781447968238
ISBN
1447968239
Related Titles


Product detail

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9781447968238
Graphical Approach to Precalculus with Limits Pearson New International Edition, plus MyMathLab without eText
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Description

A Graphical Approach to Precalculus with Limits: A Unit Circle Approach illustrates how the graph of a function can be used to support the solutions of equations and inequalities involving the function. Beginning with linear functions in Chapter 1, the text uses a four-part process to analyze each type of function, starting first with the graph of the function, then the equation, the associated inequality of that equation, and ending with applications. The text covers all of the topics typically caught in a college algebra course, but with an organization that fosters students’ understanding of the interrelationships among graphs, equations, and inequalities.

 

With the Fifth Edition, the text continues to evolve as it addresses the changing needs of today’s students. Included are additional components to build skills, address critical thinking, solve applications, and apply technology to support traditional algebraic solutions, while maintaining its unique table of contents and functions-based approach. A Graphical Approach to Precalculus with Limits: A Unit Circle Approach continues to incorporate an open design, with helpful features and careful explanations of topics.

Features

  • Chapter openers provide a Chapter Outline and a motivating application topic that is tied to the chapter content.
  • Enhanced examples have replaced many examples in this edition. All solutions have been carefully polished to incorporate more side comments.
  • Dual-Solution Format displays selected examples with side-by-side analytic and graphing calculator solutions, to connect traditional analytic methods for solving problems with graphical methods of solution or support. Some of these examples are marked with the graphing calculator icon to indicate that additional information on the graphing calculator solution is included in the Graphing Calculator Manual that accompanies the text.
  • Pointers direct students to comments that include on-the-spot reminders and warnings about common pitfalls.
  • Highlighted section and figure references within the text are shown using boldface type when referring to numbered sections (e.g., Section 2.1) and the corresponding font when referring to numbered figures (e.g., Figure 1).
  • Figures and photos appeal to today’s students who are more visually oriented than ever. As a result, more figures, diagrams, tables, and graphs, including the “hand-drawn” style of graphs are provided whenever possible. Photos accompany applications in examples and exercises.
  • Function Capsule boxes offer a comprehensive, visual introduction to each class of function and serve as an excellent resource for reference and review. Each capsule includes traditional and calculator graphs and a calculator table of values, as well as the domain, range, and other specific information about the function. Abbreviated versions of function capsules are provided on the inside back cover of the text.
  • What Went Wrong? features anticipate typical errors that students make when using graphing technology and provides an avenue for instructors to highlight and discuss such errors. Answers are included on the same page as the “What Went Wrong?” boxes.
  • Cautions andNotes warn students of common errors and emphasize important ideas throughout the exposition.
  • Looking Ahead to Calculus are margin notes that provide glimpses of how the algebraic topics currently being studied are used in calculus.
  • Technology Notes appear in the margin and provide tips to students on how to use graphing calculators more effectively. Some notes are marked with a graphing calculator icon to indicate that additional related information on graphing technology is included in the Graphing Calculator Manual that accompanies the text.
  • For Discussion activities appear within the exposition or in the margins and offer material on important concepts for instructors and students to investigate or discuss in class.
  • Exercise sets include hundreds of new and revised exercises that provide students with ample opportunities to practice, apply, connect, and extend concepts and skills. Exercises include writing exercises as well as multiple-choice, matching, true/ false, and completion problems. Exercises marked Concept Checkfocus on mathematical thinking and conceptual understanding, while those marked Checking Analytic Skills are intended for students to solve without the use of a calculator. Real data has been updated throughout.
  • Relating Concepts groups of exercises appear in selected exercise sets. They tie together topics and highlight relationships among various concepts and skills. All answers to these problems appear in the answer section at the back of the student book.
  • Reviewing Basic Concepts sets of exercises appear every two or three sections and allow students to review and check their understanding of the material in preceding sections. All answers to these problems are included in the answer section at the back of the student book.
  • Chapter review material appears in each end-of-chapter Summary and features a section-by-section list of Key Terms and Symbols, in addition to Key Concepts. A comprehensive set of Chapter Review Exercises and a Chapter Test are also included.

New to this Edition

Hundreds of exercises are new or revised, many of which are devoted to skill development.

·  Examples and exercises throughout include new and updated applications that use current, real-world data.

·  Enhanced Examples have replaced many examples in this edition. All solutions have been carefully polished to incorporate more side comments.

·  Expanded coverage of graphing by hand appears throughout the text. Many additional graphs have been incorporated featuring a “hand-drawn” style that simulates what a student might actually sketch on graph paper into discussions and examples.

·  A subsection on division of any two polynomials has been added (Section 3.6).

·  More discussion and exercises involving factoring polynomials of higher degree are now included (Section 3.7).

·  A subsection on graphing rational functions that have no vertical asymptotes has been added (Section 4.2).

·  Rate-of-work problems as illustrations of applications of rational equations have been added (Section 4.3).

·  Inverse functions section now includes discussion of inverses of rational functions (Section 5.1).

·  Material on solving logarithmic inequalities and equations quadratic in form, where u = ex is now included (Section 5.5).

·  Chapter 5 now concludes with a set of summary exercises, covering the first five chapters and focusing on domains, defining equations, and composition of the various classes of functions discussed up to that point.

·  Increased opportunity for solving linear systems graphically without the use of a calculator (Section 7.1).

·  Expanded the discussion of matrix inverses (Section 7.6).

·  Reordered the section on Counting Theory to precede coverage of the binomial theorem and mathematical induction in Chapter 8.

Table of Contents

Chapter 1  Linear Functions, Equations, and Inequalities 

1.1  Real Numbers and the Rectangular Coordinate System

1.2  Introduction to Relations and Functions

Reviewing Basic Concepts

1.3  Linear Functions

1.4  Equations of Lines and Linear Models

Reviewing Basic Concepts

1.5  Linear Equations and Inequalities

1.6  Applications of Linear Functions 

Reviewing Basic Concepts

Summary

Review Exercises

Test

 

Chapter 2  Analysis of Graphs of Functions

2.1  Graphs of Basic Functions and Relations; Symmetry

2.2  Vertical and Horizontal Shifts of Graphs   

2.3  Stretching, Shrinking, and Reflecting Graphs

Reviewing Basic Concepts

2.4  Absolute Value Functions

2.5  Piecewise-Defined Functions

2.6  Operations and Composition

Reviewing Basic Concepts

 

Summary

Review Exercises

Test

 

  

Chapter 3  Polynomial Functions

3.1  Complex Numbers

3.2  Quadratic Functions and Graphs

3.3  Quadratic Equations and Inequalities

Reviewing Basic Concepts

3.4  Further Applications of Quadratic Functions and Models

3.5  Higher-Degree Polynomial Functions and Graphs

Reviewing Basic Concepts

3.6  Topics in the Theory of Polynomial Functions (I)

3.7  Topics in the Theory of Polynomial Functions (II)

3.8  Polynomial Equations and Inequalities;  Further Applications and Models

Reviewing Basic Concepts

 

Summary

Review Exercises

Test

 

Chapter 4  Rational, Power, and Root Functions

4.1  Rational Functions and Graphs

4.2  More on Rational Functions and Graphs

4.3  Rational Equations, Inequalities, Models, and Applications

Reviewing Basic Concepts

4.4  Functions Defined by Powers and Roots

4.5  Equations, Inequalities, and Applications Involving Root Functions

Reviewing Basic Concepts

 

Summary

Review Exercises

Test

  

Chapter 5  Inverse, Exponential, and Logarithmic Functions

5.1  Inverse Functions

5.2  Exponential Functions

5.3  Logarithms and Their Properties

Reviewing Basic Concepts

5.4  Logarithmic Functions

5.5  Exponential and Logarithmic Equations and Inequalities

Reviewing Basic Concepts

5.6  Further Applications and Modeling with Exponential and Logarithmic Functions

 

Summary

Review Exercises

Test

  

Chapter 6  Analytic Geometry

6.1  Circles and Parabolas

6.2  Ellipses and Hyperbolas

Reviewing Basic Concepts

6.3  Summary of Conic Sections

6.4  Parametric Equations 

Reviewing Basic Concepts

 

Summary

Review Exercises

Test   

  

Chapter 7  Systems of Equations and Inequalities; Matrices

7.1  Systems of Equations

7.2  Solution of Linear Systems in Three Variables

7.3  Solution of Linear Systems by Row Transformations

Reviewing Basic Concepts

7.4  Matrix Properties and Operations

7.5  Determinants and Cramer’s Rule

7.6  Solution of Linear Systems by Matrix Inverses

Reviewing Basic Concepts

7.7  Systems of Inequalities and Linear Programming

7.8  Partial Fractions

Reviewing Basic Concepts

 

Summary

Review Exercises

Test   

 

Chapter 8 The Unit Circle and the Functions of Trigonometry

8.1 Angles, Arcs, and Their Measures

8.2 The Unit Circle and Its Functions

Reviewing Basic Concepts

8.3 Graphs of the Sine and Cosine Functions

Periodic Functions

8.4 Graphs of the Other Circular Functions

8.5 Functions of Angles and Fundamental Identities

8.6 Evaluating Trigonometric Functions

Definitions of the Trigonometric Functions

8.7 Applications of Right Triangles

8.8 Harmonic Motion

Reviewing Basic Concepts

Summary

Review Exercises

Test

 

Chapter 9 Trigonometric Identities and Equations

9.1 Trigonometric Identities

9.2 Sum and Difference Identities

Reviewing Basic Concepts

9.3 Further Identities   

9.4 The Inverse Circular Functions

Reviewing Basic Concepts

9.5 Trigonometric Equations and Inequalities (I)

9.6 Trigonometric Equations and Inequalities (II)

Summary

Review Exercises

Test

 

Chapter 10  Applications of Trigonometry and Vectors

10.1 The Law of Sines

10.2 The Law of Cosines and Area Formulas   

10.3 Vectors and Their Applications

Reviewing Basic Concepts

10.4 Trigonometric (Polar) Form of Complex Numbers

10.5 Powers and Roots of Complex Numbers

Reviewing Basic Concepts

10.6 Polar Equations and Graphs

10.7 More Parametric Equations

Reviewing Basic Concepts

Summary

Review Exercises

Test

 

Chapter 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  Probability

 

Chapter 12  Limits, Derivatives, and Definite Integrals

12.1  An Introduction to Limits

12.2  Techniques for Calculating Limits

12.3  One-Sided Limits; Limits Involving Infinity

12.4  Tangent Lines and Derivatives

12.5  Area and the Definite Integral

 

Chapter R  Reference:  Basic Algebraic Concepts

R.1  Review of Exponents and Polynomials

R.2  Review of Factoring

R.3  Review of Rational Expressions

R.4  Review of Negative and Rational Exponents

R.5  Review of Radicals

Chapter R Test

 

Appendix Geometry Formulas

Answers to Selected Exercises

Index