Graphical Approach to Algebra and Trigonometry, A, CourseSmart eTextbook, 5th Edition

Published Date: Mar 15, 2010

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Description

A Graphical Approach to Algebra and Trigonometry 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 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.
CourseSmart textbooks do not include any media or print supplements that come packaged with the bound book.

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

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

Chapter R Test

Summary

Review Exercises

Test

Appendix Geometry Formulas