Graphical Approach to Algebra and Trigonometry, A

by Hornsby, John; Lial, Margaret L.; Rockswold, Gary K.

• ISBN13: 9780321644725
• ISBN10: 0321644727
• Edition: 5th
• Format: Hardcover
• Copyright: 2010-01-27
• Publisher: Pearson

Summary

Key Benefit: AGraphical Approach to Algebra and Trigonometryillustrates 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 studentsrs" understanding of the interrelationships among graphs, equations, and inequalities. With theFifth Edition,the text continues to evolve as it addresses the changing needs of todayrs"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.AGraphical Approach to Algebra and Trigonometry continues to incorporate an open design, with helpful features, careful explanations of topics, and a comprehensive package of supplements and study aids to provide new and relevant opportunities for learning and teaching. Key Topics: Linear Functions, Equations, and Inequalities, Real Numbers and the Rectangular Coordinate System, Introduction to Relations and Functions, Linear Functions, Equations of Lines and Linear Models, Linear Equations and Inequalities, Applications of Linear Functions, Analysis of Graphs of Functions, Graphs of Basic Functions and Relations; Symmetry, Vertical and Horizontal Shifts of Graphs, Stretching, Shrinking, and Reflecting Graphs, Absolute Value Functions, Piecewise-Defined Functions, Operations and Composition, Polynomial Functions, Complex Numbers, Quadratic Functions and Graphs, Quadratic Equations and Inequalities, Further Applications of Quadratic Functions and Models, Higher-Degree Polynomial Functions and Graphs, Topics in the Theory of Polynomial Functions (I), Topics in the Theory of Polynomial Functions (II), Polynomial Equations and Inequalities; Further Applications and Models, Rational, Power, and Root Functions, Rational Functions and Graphs, More on Rational Functions and Graphs, Rational Equations, Inequalities, Models, and Applications, Functions Defined by Powers and Roots, Equations, Inequalities, and Applications Involving Root Functions, Inverse, Exponential, and Logarithmic Functions, Inverse Functions, Exponential Functions, Logarithms and Their Properties, Logarithmic Functions, Exponential and Logarithmic Equations and Inequalities, Further Applications and Modeling with Exponential and Logarithmic Functions, Analytic Geometry, Circles and Parabolas, Ellipses and Hyperbolas, Summary of Conic Sections, Parametric Equations, Systems of Equations and Inequalities; Matrices, Systems of Equations, Solution of Linear Systems in Three Variables, Solution of Linear Systems by Row Transformations, Matrix Properties and Operations, Determinants and Cramerrs"s Rule, Solution of Linear Systems by Matrix Inverses, Systems of Inequalities and Linear Programming, Partial Fractions, Further Topics in Algebra, Sequences and Series, Arithmetic Sequences and Series, Geometric Sequences and Series, Counting Theory, The Binomial Theorem, Mathematical Induction, Probability, Reference: Basic Algebraic Concepts, Review of Exponents and Polynomials, Review of Factoring, Review of Rational Expressions, Review of Negative and Rational Exponents, Review of Radicals, Appendix Geometry Formulas Market Description:Intended for those who are interested in gaining a basic knowledg

Author Biography

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 has always been interested in math; it was her favorite subject in the first grade! Marge's intense desire to educate both her students and herself has inspired the writing of numerous best-selling textbooks. Marge, who received Bachelor's and Master's degrees from California State University at Sacramento, is now affiliated with American River College.

 

Marge is an avid reader and traveler. Her travel experiences often find their way into her books as applications, exercise sets, and feature sets. She is particularly interested in archeology. Trips to various digs and ruin sites have produced some 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. He is currently employed at Minnesota State University, Mankato, where he is a full professor of mathematics. 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.

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 Trigonometric Functions and Their Applications

8.1 Angles and Their Measures

8.2 Trigonometric Functions and Fundamental Identities

Reviewing Basic Concepts

8.3 Evaluating Trigonometric Functions     

8.4 Applicationis of Right Triangles

Reviewing Basic Concepts

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

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

Review Exercises

Test

 

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

Summary

Review Exercises

Test

 

Appendix Geometry Formulas

Answers to Selected Exercises

Index