by Arthur Goodman and Lewis Hirsch

ISBN13: 978-0534371760

ISBN10: 0534371760

Cover type:

Edition/Copyright: REV 00

Publisher: Brooks/Cole Publishing Co.

Published: 2000

International: No

ISBN10: 0534371760

Cover type:

Edition/Copyright: REV 00

Publisher: Brooks/Cole Publishing Co.

Published: 2000

International: No

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Goodman and Hirsch's Precalculus: Understanding Functions: A Graphing Approach is a graphing calculator-dependent book that offers a strong problem-solving focus. These experienced authors have been praised for their in-depth explanations and their commitment to avoiding a cookbook approach. Their book emphasizes the importance of good study skills and the need for thoughtful integration of the graphing calculator.

**1. ALGEBRA: THE FUNDAMENTALS. **

The Real Numbers. Operations with Real Numbers. Polynomials and Rational Expressions. Exponents and Radicals. The Complex Numbers. First Degree Equations and Inequalities in One Variable. Absolute Value Equations and Inequalities. Quadratic Equations and Equations in Quadratic Form. Quadratic and Rational Inequalities. Substitution. Review Exercises, Practice Test.

**2. FUNCTIONS AND GRAPHS: PART I. **

The Cartesian Coordinate System: Graphing Straight Lines and Equations of Circles. Slope. Equations of a Line. Relations and Functions. Function Notation. Relating Equations to Their Graphs. Introduction to Graph Sketching: Symmetry. Chapter Summary, Review Exercises, Practice Test.

**3. FUNCTIONS AND GRAPHS: PART II. **

Basic Graphing Principles. More Graphing Principles; Types of Functions. Extracting Functions from "Real Life" Situations. Quadratic Functions. Operations on Functions. Inverse Functions. Chapter Summary, Review Exercises, Practice Test.

**4. POLYNOMIAL, RATIONAL, AND RADICAL FUNCTIONS. **

Polynomial Functions. More Polynomial Functions and Mathematical Models. Polynomial Division and Synthetic Division. Roots of Polynomial Equations: The Factor, Remainder, and Rational Root Theorems. Rational Functions. Radical Functions. Variation. Chapter Summary, Review Exercises, Practice Test.

**5. EXPONENTIAL AND LOGARITHMIC FUNCTIONS. **

Exponential Functions. Logarithmic Functions. Properties of Logarithms; Logarithm Equations. Common and Natural Logarithms; Exponential Equations and Change of Base. Applications. Chapter Summary, Review Exercises, Practice Test.

**6. TRIGONOMETRY. **

Angle Measurement and Two Special Triangles. The Trigonometric Functions of a General Angle. Right Triangle Trigonometry and Applications. The Trigonometric Functions as Functions of Real Numbers. Chapter Summary, Review Exercises, Practice Test.

**7. THE TRIGONOMETRIC FUNCTIONS. **

The Sine and Cosine Functions and Their Graphs. The Tangent, Secant, Cosecant, and Cotangent Functions and Their Graphs. Basic Identities. Trigonometric Equations. The Inverse Trigonometric Functions. Chapter Summary, Review Exercises, Practice Test.

**8. MORE TRIGONOMETRY AND ITS APPLICATIONS. **

The Addition Formulas. The Double-Angle and Half-Angle Formulas. The Law of Sines and the Law of Cosines. The Trigonometric Form of Complex Numbers and DeMoivre's Theorem. Chapter Summary, Review Exercises, Practice Test.

**9. SYSTEMS OF EQUATIONS AND INEQUALITIES. **

Elimination and Substitution: 2 x 2 Linear Systems. Elimination and Gaussian Elimination: 3 x 3 Linear Systems. Solving Linear Systems Using Augmented Matrices. Determinants and Cramer's Rule: 2 x 2 and 3 x 3 Systems. Systems of Linear Inequalities. Chapter Summary, Review Exercises, Practice Test.

**10. THE CONIC SECTIONS. **

Conic Sections: Circles. The Parabola. The Ellipse. The Hyperbola. Identifying Conic Sections and Degenerate Forms. Non-Linear Systems of Equations and Inequalities. Chapter Summary, Review Exercises, Practice Test.

**11. SEQUENCES AND SERIES AND RELATED TOPICS. **

Sequences. Series and Sigma Notation. Arithmetic Sequences and Series. Geometric Sequences and Series. Mathematical Induction. Permutations and Combinations. The Binomial Theorem. Chapter Summary, Review Exercises, Practice Test.

Arthur Goodman and Lewis Hirsch

ISBN13: 978-0534371760ISBN10: 0534371760

Cover type:

Edition/Copyright: REV 00

Publisher: Brooks/Cole Publishing Co.

Published: 2000

International: No

Goodman and Hirsch's Precalculus: Understanding Functions: A Graphing Approach is a graphing calculator-dependent book that offers a strong problem-solving focus. These experienced authors have been praised for their in-depth explanations and their commitment to avoiding a cookbook approach. Their book emphasizes the importance of good study skills and the need for thoughtful integration of the graphing calculator.

Table of Contents

**1. ALGEBRA: THE FUNDAMENTALS. **

The Real Numbers. Operations with Real Numbers. Polynomials and Rational Expressions. Exponents and Radicals. The Complex Numbers. First Degree Equations and Inequalities in One Variable. Absolute Value Equations and Inequalities. Quadratic Equations and Equations in Quadratic Form. Quadratic and Rational Inequalities. Substitution. Review Exercises, Practice Test.

**2. FUNCTIONS AND GRAPHS: PART I. **

The Cartesian Coordinate System: Graphing Straight Lines and Equations of Circles. Slope. Equations of a Line. Relations and Functions. Function Notation. Relating Equations to Their Graphs. Introduction to Graph Sketching: Symmetry. Chapter Summary, Review Exercises, Practice Test.

**3. FUNCTIONS AND GRAPHS: PART II. **

Basic Graphing Principles. More Graphing Principles; Types of Functions. Extracting Functions from "Real Life" Situations. Quadratic Functions. Operations on Functions. Inverse Functions. Chapter Summary, Review Exercises, Practice Test.

**4. POLYNOMIAL, RATIONAL, AND RADICAL FUNCTIONS. **

Polynomial Functions. More Polynomial Functions and Mathematical Models. Polynomial Division and Synthetic Division. Roots of Polynomial Equations: The Factor, Remainder, and Rational Root Theorems. Rational Functions. Radical Functions. Variation. Chapter Summary, Review Exercises, Practice Test.

**5. EXPONENTIAL AND LOGARITHMIC FUNCTIONS. **

Exponential Functions. Logarithmic Functions. Properties of Logarithms; Logarithm Equations. Common and Natural Logarithms; Exponential Equations and Change of Base. Applications. Chapter Summary, Review Exercises, Practice Test.

**6. TRIGONOMETRY. **

Angle Measurement and Two Special Triangles. The Trigonometric Functions of a General Angle. Right Triangle Trigonometry and Applications. The Trigonometric Functions as Functions of Real Numbers. Chapter Summary, Review Exercises, Practice Test.

**7. THE TRIGONOMETRIC FUNCTIONS. **

The Sine and Cosine Functions and Their Graphs. The Tangent, Secant, Cosecant, and Cotangent Functions and Their Graphs. Basic Identities. Trigonometric Equations. The Inverse Trigonometric Functions. Chapter Summary, Review Exercises, Practice Test.

**8. MORE TRIGONOMETRY AND ITS APPLICATIONS. **

The Addition Formulas. The Double-Angle and Half-Angle Formulas. The Law of Sines and the Law of Cosines. The Trigonometric Form of Complex Numbers and DeMoivre's Theorem. Chapter Summary, Review Exercises, Practice Test.

**9. SYSTEMS OF EQUATIONS AND INEQUALITIES. **

Elimination and Substitution: 2 x 2 Linear Systems. Elimination and Gaussian Elimination: 3 x 3 Linear Systems. Solving Linear Systems Using Augmented Matrices. Determinants and Cramer's Rule: 2 x 2 and 3 x 3 Systems. Systems of Linear Inequalities. Chapter Summary, Review Exercises, Practice Test.

**10. THE CONIC SECTIONS. **

Conic Sections: Circles. The Parabola. The Ellipse. The Hyperbola. Identifying Conic Sections and Degenerate Forms. Non-Linear Systems of Equations and Inequalities. Chapter Summary, Review Exercises, Practice Test.

**11. SEQUENCES AND SERIES AND RELATED TOPICS. **

Sequences. Series and Sigma Notation. Arithmetic Sequences and Series. Geometric Sequences and Series. Mathematical Induction. Permutations and Combinations. The Binomial Theorem. Chapter Summary, Review Exercises, Practice Test.

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