Understanding Algebra for College Students/ Hirsch and Goodman

TABLE OF CONTENTS

1. THE FUNDAMENTAL CONCEPTS.1
Basic Definitions: The Real Numbers and the Real Number Lin
Operations and Real Numbers.
Algebraic Expressions.
Translating Phrases and Sentences into Algebraic Form.
First-Degree Equations and Inequalities.
Chapter Summary, Review Exercises, and Practice Test.

2. EQUATIONS AND INEQUALITIES.55

Equations as Mathematical Models.
First-Degree Equations and Applications.
First-Degree Inequalities and Applications.
Absolute-Value Equations and Inequalities.
Chapter Summary, Review Exercises, and Practice Test.

3. GRAPHING STRAIGHT LINES AND FUNCTIONS.105

The Rectangular Coordinate System and Graphing Straight Lines.
Graphs and Equations.
Relations and Functions: Basic Concepts.
Function Notation.
Interpreting Graphs.
Chapter Summary, Review Exercises, and Practice Test.
Cumulative Review and Practice Test: Chapters 1-3.

4. EQUATIONS OF A LINE AND LINEAR SYSTEMS IN TWO VARIABLES.178

Straight Lines and Slope.
Equations of a Line and Linear Functions as Mathematical Models.
Linear Systems in Two Variables.
Graphing Linear Inequalities in Two Variables.
Chapter Summary, Review Exercises, and Practice Test.

5. POLYNOMIAL FUNCTIONS.235

Polynomial Functions as Mathematical Models.
Polynomials: Sums, Differences, and Products.
General Forms and Special Products.
Factoring out the Greatest Common Factor.
Factoring Trinomials.
Solving Polynomial Equations by Factoring and Graphing.
Polynomial Division.
Chapter Summary, Review Exercises, and Practice Test.

6. RATIONAL EXPRESSIONS AND FUNCTIONS 283.

Equivalent Fractions.
Multiplication and Division of Rational Expressions.
Sums and Differences of Rational Expressions.
Mixed Operations and Complex Fractions.
Fractional Equations and Inequalities.
Literal Equations. Rational Functions and Equations as Mathematical Models.
Chapter Summary, Review Exercises, and Practice Test.
Cumulative Review and Practice Test: Chapters 4-6.

7. EXPONENTS AND RADICALS.337

Natural Number and Integer Exponents.
Scientific Notation.
Rational Exponents and Radical Notation.
Simplifying Radical Expressions.
Adding and Subtracting Radical Expressions.
Multiplying and Dividing Radical Expressions.
Radical Functions and Equations.
Complex Numbers.
Chapter Summary, Review Exercises, and Practice Test.

8. QUADRATIC FUNCTIONS.400

Quadratic Functions as Mathematical Models.
Solving Quadratic Equations: The Factoring and Square Root Methods.
Solving Quadratic Equations: Completing the Square.
Solving Quadratic Equations: The Quadratic Formula.
Equations Reducible to Quadratic Form (and More Radical Equations).
Graphing Quadratic Functions.
Quadratic and Rational Inequalities.
The Distance Formula: Circles.
Chapter Summary, Review Exercises, and Practice Test.

9. MORE ON FUNCTIONS.487

More on Function Notation: Split Functions.
Composition and the Algebra of Functions.
Types of Functions.
Inverse Functions.
Variation.
Chapter Summary, Review Exercises, and Practice Test.
Cumulative Review and Practice Test: Chapters 7-9.

10. EXPONENTIAL AND LOGARITHMIC FUNCTIONS.533

Exponential Functions.
Logarithms.
Properties of Logarithms.
Common Logarithms, Natural Logarithms, and Change of Base.
Exponential and Logarithmic Equations.
Applications: Exponential and Logarithmic Functions as Mathematical Models.
Chapter Summary, Review Exercises, and Practice Test.

11. MORE SYSTEMS OF EQUATIONS AND SYSTEMS OF INEQUALITIES.577

3x3 Linear Systems.
Solving Linear Systems Using Augmented Matrices.
The Algebra of Matrices.
Solving Linear Systems Using Matrix Inverses.
Determinants and Cramer's Rule.
Systems of Linear Inequalities.
Nonlinear Systems of Equations.
Chapter Summary, Review Exercises, and Practice Test.

12. SEQUENCES AND SERIES: THE BINOMIAL THEOREM.647

Sequences.
Series and Sigma Notation.
Arithmetic Sequences and Series.
Geometric Sequences and Series.
The Binomial Theorem.
Cumulative Review and Practice Test: Chapters 10-12.


APPENDIX A: Sets. 691
APPENDIX B: The Conic Sections.696

Answers to Selected Exercises and Chapter Tests. 714

INDEX.761