Precalculus - Understanding Functions A Graphing Approach

ISBN-10: 0534386350
ISBN-13: 9780534386351
Edition: 2nd 2004 (Revised)
List price: $318.95 Buy it from $3.00
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Description: These experienced authors have been praised for their in-depth explanations and their commitment to avoiding a cookbook approach. Their text addresses three critical issues in teaching precalculus: poor student preparation, the need for thoughtful  More...

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Book details

List price: $318.95
Edition: 2nd
Copyright year: 2004
Publisher: Brooks/Cole
Publication date: 10/17/2003
Binding: Hardcover
Pages: 975
Size: 8.50" wide x 9.75" long x 1.50" tall
Weight: 4.334
Language: English

These experienced authors have been praised for their in-depth explanations and their commitment to avoiding a cookbook approach. Their text addresses three critical issues in teaching precalculus: poor student preparation, the need for thoughtful integration of the graphing calculator, and poor student study skills. Their texts have a strong reputation built on mathematically sound presentation, excellent applications, and on challenging students to develop algebraic, graphical, and verbal mathematical skills. Goodman and Hirsch help students go beyond the mechanics of mathematics to developing a coherent strategy to solving problems.

Dr. Arthur Goodman (Ph.D., Yeshiva University) currently teaches in the mathematics department at Queens College of the City University of New York. Dr. Goodman takes great pride in the mathematical accuracy and in depth explanation in all of his textbooks.

Lewis Hirsch (Ph.D., Pennsylvania State University) currently teaches in the mathematics department at Rutgers University. Dr. Hirsch teaches both developmental mathematics and higher level courses such as college algebra and pre-calculus. His experiences in the classroom make him committed to properly preparing students in lower-level courses so they can succeed in for credit courses, and this is reflected in the way he writes his textbooks.

Preface
Algebra: The Fundamentals
The Real Numbers
Different Perspectives: Inequalities
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
Different Perspectives: Absolute Value Equations and Inequalities
Quadratic Equations and Equations in Quadratic Form
Quadratic and Rational Inequalities
Substitution
Review Exercises
Practice Test
Functions and Graphs: Part I
The Cartesian Coordinate System: Graphing Straight Lines and Circles
Different Perspectives: The Graph of an Equation
Different Perspectives: Intercepts
Slope
Equations of a Line
Technology Corner
Relations and Functions
Different Perspectives: Representing Relations
Different Perspectives: Functions
Function Notation
Different Perspectives: Function Notation
Relating Functions to Their Graphs
Different Perspectives: Solving f(x) = k
Different Perspectives: The Zeros of a Function
Different Perspectives: Solving Inequalities
Introduction to Graph Sketching: Symmetry
Different Perspectives: Symmetry
Summary
Review Exercises
Practice Test
Functions and Graphs: Part II
Basic Graphing Principles
Different Perspectives: The Vertical Shift Principle
Different Perspectives: The Horizontal Shift Principle
Technology Corner
More Graphing Principles: Types of Functions
Extracting Functions from Real-Life Situations
Quadratic Functions
Operations on Functions
Technology Corner
Inverse Functions
Different Perspectives: One-to-One Functions
Summary
Review Exercises
Practice Test
Polynomial, Rational, and Radical Functions
Polynomial Functions
Different Perspectives: End Behavior
More on Polynomial Functions and Mathematical Models
Polynomial Division, Roots of Polynomial Equations: The Remainder and Factor Theorems
Roots of Polynomial Equations (continued): The Rational Root Theorem and Descartes' Rule of Signs
Rational Functions
Radical Functions
Variation
Summary
Review Exercises
Practice Test
Exponential and Logarithmic Functions
Exponential Functions
Logarithmic Functions
Properties of Logarithms; Logarithmic Equations
Common and Natural Logarithms; Exponential Equations and Change of Base
Applications
Summary
Review Exercises
Practice Test
Interim Review 1 (Chapters 1-5)
Trigonometry
Angle Measurement and Two Special Triangles
Technology Corner
The Trigonometric Functions
Right-Triangle Trigonometry and Applications
The Trigonometric Functions as Functions of Real Numbers
Summary
Review Exercises
Practice Test
The Trigonometric Functions
The Sine and Cosine Functions and Their Graphs
The Tangent, Secant, Cosecant, and Cotangent Functions
Basic Identities
Trigonometric Equations
Different Perspectives: Trigonometric Equations
The Inverse Trigonometric Functions
Summary
Review Exercises
Practice Test
More Trigonometry and Its Applications
The Addition Formulas
The Double-Angle and Half-Angle Formulas
The Law of Sines and the Law of Cosines
Vectors
The Trigonometric Form of Complex Numbers and DeMoivre's Theorem
Polar Coordinates
Summary
Review Exercises
Practice Test
Interim Review 2 (Chapters 6-8)
Systems of Linear Equations and Inequalities
2 x 2 Linear Systems: Elimination and Substitution
3 x 3 Linear Systems: Elimination and Gaussian Elimination
Solving Linear Systems Using Augmented Matrices
The Algebra of Matrices
Solving Linear Systems Using Matrix Inverses
Determinants and Cramer's Rule: 2 x 2 and 3 x 3 Systems
Properties of Determinants
Systems of Linear Inequalities
An Introduction to Linear Programming: Geometric Solutions
Summary
Review Exercises
Practice Test
Conic Sections and Nonlinear Systems
Conic Sections: Circles
The Parabola
The Ellipse
Different Perspectives: Eccentricity
The Hyperbola
Identifying Conic Sections: Degenerate Forms
Translations and Rotations of Coordinate Axes
Nonlinear Systems of Equations and Inequalities
Summary
Review Exercises
Practice Test
Sequences, 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
Summary
Review Exercises
Practice Test
Using Technology to Model Data
Answers to Selected Exercises
Index of Applications
Index

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