A Graphical Approach to Algebra and Trigonometry

Series
Pearson
Author
John Hornsby / Margaret L. Lial / Gary K. Rockswold  
Publisher
Pearson
Cover
Softcover
Edition
6
Language
English
Total pages
1024
Pub.-date
December 2013
ISBN13
9780321927330
ISBN
0321927338


Textbook

Product Price CHF Available  
9780321927330
A Graphical Approach to Algebra and Trigonometry
278.20 approx. 7-9 days

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Description

Note: You are purchasing a standalone product; MyMathLab does not come packaged with this content. If you would like to purchase both the physical text and MyMathLab, search for

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0321927338 / 9780321927330 A Graphical Approach to Algebra and Trigonometry

 

MyMathLab is not a self-paced technology and should only be purchased when required by an instructor.


Hornsby/Lial/Rockswold’s Graphical Approach covers functions through a consistent four part analytical process that asks students to 1) Examine the nature of the graph 2) Solve a typical equation analytically and graphically 3) Solve the related inequality analytically and graphically, and finally, 4) Apply analytic and graphical methods to solve an application of that class of function.

 

To provide a better teaching and learning experience for both instructors and students, this program will:

  • Improve Results with MyMathLab: MyMathLab delivers proven results in helping students succeed and provides engaging experiences that personalize learning.
  • Build students’ analytical skills: The authors’ consistent four step process helps students gain a deep visual and graphical understanding of math, solidifying a stronger connection to the mathematical world around them.
  • The visualizations throughout the text have been enhanced to increase students’ comprehension of core algebra and trigonometry concepts.
  • Updated chapters provide students with clear explanations, examples and data: New chapter updates present explanations, exercisesand examples to ensure that students will truly comprehend and retain information.  

 

Features

Improve Results with MyMathLab: MyMathLab delivers proven results in helping students succeed and provides engaging experiences that personalize learning.

  • NEW! Getting Ready skill review quizzes are assignable throughout the course, testing students on prerequisite knowledge. Each student receives a personalized homework assignment to refresh forgotten concepts based on quiz results.
  • NEW! Adaptive Study Plan makes studying more efficient and effective for every student.  Performance and activity are assessed continually in real time. Data and analytics are used to provide personalized content—reinforcing concepts that target each student's strengths and weaknesses. 
  • NEW! Video Assessment exercises are available with key Example/Solution videos to check students’ conceptual understanding of important math concepts.
  • NEW! Skills for Success Module supports students toward continued success in college. This module provides tutorials and guidance on topics such as transitioning to college, online learning, time management and more. Additionally, there is content to help students with professional skills such as resume development and interview preparation.
  • NEW! Reviewing Basic Concepts exercises are now assignable in MyMathLab. The exercise sets appear every two or three sections and allow students to review and check their understanding of the material in preceding sections.
  • NEW! Graphing Functionality allows students to graph 3-point cubic, 4-point quadratic and transformation graphs within MyMathLab exercises.

 

Build students’ analytical skills: The four-step analytical process is the foundation of the Hornsby approach. In addition, the authors build sound pedagogy to support analytical thinking. Chapter layouts, exercises, review questions and chapter features offer a comprehensive roadmap for students to follow for a successful understanding of algebra and trigonometry.

  • NEW! Chapter tests have been revised to better reflect the content that was covered.
  • NEW! More examples and exercises have been added to better prepare students for analytic skills.
  • NEW! Exercise sets have been revised so that odd and even exercises are paired appropriately.
  • NEW! Algebra Reviews occur in the margin of the text and provide “just in time” review by referring students to where they can receive additional help with important topics from algebra.
  • Pointers direct students to comments that include on-the-spot reminders and warnings about common pitfalls.
  • 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.
  • 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.
  • The What Went Wrong? feature anticipates 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 and Notes warn students of common errors and emphasize important ideas throughout the exposition.
  • 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 Check focus 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.
  • Looking Ahead to Calculus are margin notes that provide glimpses of how the algebraic topics currently being studied are used in calculus.
  • Relating Concepts exercises appear in select 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.

 

The visualizations throughout the text have been enhanced to increase students’ comprehension of core algebra and trigonometry concepts.

  • NEW! Data has been updated to increase student interest in mathematics. Some new application topics include half-life of a Twitter link, iPads®, social networks, accuracy of professional golfers, and smart phone demographics.
  • NEW! The text has more titles on graphs, captions, pointers (bubbles), color, and side comments to increase clarity and understanding for students.
  • 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.

 

New to this Edition

Updates to the MyMathLab Course

  • Ready-to-Go MyMathLab courses are pre-built MyMathLab courses that make the start-up time building your course quick and easy.  These include author-designated assignments, and more.
  • Getting Ready skill review quizzes are assignable throughout the course, testing students on prerequisite knowledge. Each student receives a personalized homework assignment to refresh forgotten concepts based on quiz results.
  • Adaptive Study Plan makes studying more efficient and effective for every student.  Performance and activity are assessed continually in real time. Data and analytics are used to provide personalized content-- reinforcing concepts that target each student's strengths and weaknesses. 
  • Video Assessment exercises are available with videos to check students’ conceptual understanding of important math concepts.
  • Skills for Success Module supports students toward continued success in college. This module provides tutorials and guidance on topics such as transitioning to college, online learning, time management and more. Additionally, there is content to help students develop professional skills such as resume development and interview preparation.
  • Graphing Functionality allows students to graph 3-point cubic, 4-point quadratic and transformation graphs within MyMathLab exercises.

 

New and Updated in the Text

  • Chapter tests have been revised to better reflect the content that was covered.
  • More examples and exercises have been added to better prepare students for analytic skills.
  • Data has been updated to increase student interest in mathematics. Some new application topics include half-life of a Twitter link, iPads®, social networks, accuracy of professional golfers, and smart phone demographics.
  • The text has more titles on graphs, captions, pointers (bubbles), color, and side comments to increase clarity and understanding for students.

 

Content Updates provide students with clear explanations, examples and real data

  • Chapter One has increased emphasis on evaluating function notation, interpreting slope as a rate of change, and evaluating average rate of change using graphs.
  • Chapter Two has clearer explanations of how to transform graphs and also how to write transformations in terms of function notation. Additional exercises covering the domain and range of shifted functions have been included.
  • Chapter Three includes more examples and exercise that cover curve fitting by hand, solving quadratic equations by completing the square, and solving polynomial equations and inequalities.
  • Chapter Four includes an increased discussion of limit notation near asymptotes, circles, horizontal parabolas, rational equations and inequalities, and rational expressions with fractional exponents.
  • Chapter Five has additional examples and exercises related to graphing inverse functions by hand, solving exponential equations with negative exponents, simplifying logarithmic expressions, and solving logarithmic equations.
  • Chapter Six now covers matrices and linear systems. It has updated consumer-spending applications, a 4-step process for solving linear systems, additional examples and exercises covering systems with no solution, and a new example to better explain the technique of finding partial fraction decompositions.
  • Chapter Seven now covers conic sections and nonlinear systems of equations and inequalities. Additional examples and exercises have been added.
  • Chapter Eight has additional examples and exercises to better explain writing series in summation notation, evaluating recursive sequences, and summing series.

 

Table of Contents

1. Linear Functions, Equations, and Inequalities

1.1 Real Numbers and the Rectangular Coordinate System

1.2 Introduction to Relations and Functions

1.3 Linear Functions

1.4 Equations of Lines and Linear Models

1.5 Linear Equations and Inequalities

1.6 Applications of Linear Functions

 

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

2.4 Absolute Value Functions

2.5 Piecewise-Defined Functions

2.6 Operations and Composition

 

3. Polynomial Functions

3.1 Complex Numbers

3.2 Quadratic Functions and Graphs

3.3 Quadratic Equations and Inequalities

3.4 Applications of Quadratic Functions and Models

3.5 Higher-Degree Polynomial Functions and Graphs

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

 

4. Rational, Power, and Root Functions

4.1 Rational Functions and Graphs I

4.2 Rational Functions and Graphs II

4.3 Rational Equations, Inequalities, Models, and Applications

4.4 Functions Defined by Powers and Roots

4.5 Equations, Inequalities, and Applications Involving Root Functions

 

5. Inverse, Exponential, and Logarithmic Functions

5.1 Inverse Functions

5.2 Exponential Functions

5.3 Logarithms and Their Properties

5.4 Logarithmic Functions

5.5 Exponential and Logarithmic Equations and Inequalities

5.6 Further Applications and Modeling with Exponential and Logarithmic Functions

 

6. Systems and Matrices

6.1 Systems of Equations

6.2 Solution of Linear Systems in Three Variables

6.3 Solution of Linear Systems by Row Transformations

6.4 Matrix Properties and Operations

6.5 Determinants and Cramer's Rule

6.6 Solution of Linear Systems by Matrix Inverses

6.7 Systems of Inequalities and Linear Programming

6.8 Partial Fractions

 

7. Analytic Geometry and Nonlinear Systems

7.1 Circles and Parabolas

7.2 Ellipses and Hyperbolas

7.3 The Conic Sections and Nonlinear Systems

7.4 Parametric Equations

 

8. Trigonometric Functions and Applications

8.1 Angles and Their Measures

8.2 Trigonometric Functions and Fundamental Identities

8.3 Right Triangles and Evaluating Trigonometric Functions

8.4 Applications of Right Triangles

8.5 The Circular Functions

8.6 Graphs of the Sine and Cosine Functions

8.7 Graphs of the Other Circular Functions

8.8 Harmonic Motion

 

9. Trigonometric Identities and Equations

9.1 Trigonometric Identities

9.2 Sum and Difference Identities

9.3 Further Identities

9.4 The Inverse Circular Functions

9.5 Trigonometric Equations and Inequalities (I)

9.6 Trigonometric Equations and Inequalities (II)

 

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

10.4 Trigonometric (Polar) Form of Complex Numbers

10.5 Powers and Roots of Complex Numbers

10.6 Polar Equations and Graphs

10.7 More Parametric Equations

 

11. Further Topics in Algebra

11.1 Sequences and Series

11.2 Arithmetic Sequences and Series

11.3 Geometric Sequences and Series

11.4 Counting Theory

11.5 The Binomial Theorem

11.6 Mathematical Induction

11.7 Probability

 

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

Author

 

John Hornsby: When John Hornsby enrolled as an undergraduate at Louisiana State University, he was uncertain whether he wanted to study mathematics, education, or journalism. His ultimate decision was to become a teacher, but after twenty-five years of teaching at the high school and university levels and fifteen years of writing mathematics textbooks, all three of his goals have been realized; his love for teaching and for mathematics is evident in his passion for working with students and fellow teachers as well. His specific professional interests are recreational mathematics, mathematics history, and incorporating graphing calculators into the curriculum. John’s personal life is busy as he devotes time to his family (wife Gwen, and sons Chris, Jack, and Josh). He has been a rabid baseball fan all of his life. John's other hobbies include numismatics (the study of coins) and record collecting. He loves the music of the 1960s and has an extensive collection of the recorded works of Frankie Valli and the Four Seasons.

 

Marge Lial (late) was always interested in math; it was her favorite subject in the first grade! Marge's intense desire to educate both her students and herself inspired the writing of numerous best-selling textbooks. Marge, who received Bachelor's and Master's degrees from California State University at Sacramento, was most recently affiliated with American River College. An avid reader and traveler, her travel experiences often found their way into her books as applications, exercise sets, and feature sets. She was particularly interested in archeology, and trips to various digs and ruin sites produced fascinating problems for her textbooks, involving such topics as the building of Mayan pyramids and the acoustics of ancient ball courts in the Yucatan.

 

Gary Rockswold has been teaching mathematics for 33 years at all levels from seventh grade to graduate school, including junior high and high school students, talented youth, vocational, undergraduate, and graduate students, and adult education classes. Now retired, he most recently served as professor of mathematics at Minnesota State University–Mankato. He graduated with majors in mathematics and physics from St. Olaf College in Northfield, Minnesota, where he was elected to Phi Beta Kappa. He received his Ph.D. in applied mathematics from Iowa State University. He has an interdisciplinary background and has also taught physical science, astronomy, and computer science. Outside of mathematics, he enjoys spending time with his lovely wife and two children.