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Graphical Approach to Precalculus

ISBN-10: 0321357833
ISBN-13: 9780321357830
Edition: 4th 2007 (Revised)
List price: $225.33
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Description: This edition has evolved to address the needs of todays student.nbsp;While maintaining its unique tablenbsp;of contents and functions-based approach, the text now includes additional components to build skill, address critical thinking, solve  More...

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Book details

List price: $225.33
Edition: 4th
Copyright year: 2007
Publisher: Addison Wesley
Publication date: 2/3/2006
Binding: Hardcover
Pages: 1092
Size: 9.25" wide x 10.25" long x 1.50" tall
Weight: 5.368
Language: English

This edition has evolved to address the needs of todays student.nbsp;While maintaining its unique tablenbsp;of contents and functions-based approach, the text now includes additional components to build skill, address critical thinking, solve applications, and apply technology to support traditional algebraic solutions. nbsp;It continues to incorporate an open design, 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.

Preface
Linear Functions, Equations, and Inequalities
Real Numbers and the Rectangular Coordinate System
Sets of Real Numbers
The Rectangular Coordinate System
Viewing Windows
Roots
Distance and Midpoint Formulas
Introduction to Relations and Functions
Set-Builder Notation and Interval Notation
Relations, Domain, and Range
Functions
Tables
Function Notation
Reviewing Basic Concepts (Sections 1.1 and 1.2)
Linear Functions
Basic Concepts about Linear Functions
Slope of a Line
Slope-Intercept Form of the Equation of a Line
Equations of Lines and Linear Models
Point-Slope Form of the Equation of a Line
Standard Form of the Equation of a Line
Parallel and Perpendicular Lines
Linear Models and Regression
Reviewing Basic Concepts (Sections 1.3 and 1.4)
Linear Equations and Inequalities
Solving Linear Equations
Graphical Approaches to Solving Linear Equations
Identities and Contradictions
Solving Linear Inequalities
Graphical Approaches to Solving Linear Inequalities
Three-Part Inequalities
Applications of Linear Functions
Problem-Solving Strategies
Applications of Linear Equations
Break-Even Analysis
Direct Variation
Formulas
Reviewing Basic Concepts (Sections 1.5 and 1.6)
Chapter 1 Summary
Chapter 1 Review Exercises
Chapter 1 Test
Chapter 1 Project: Predicting Heights and Weights of Athletes
Analysis of Graphs of Functions
Graphs of Basic Functions and Relations; Symmetry
Continuity
Increasing and Decreasing Functions
The Identity Function
The Squaring Function and Symmetry with Respect to the y-Axis
The Cubing Function and Symmetry with Respect to the Origin
The Square Root and Cube Root Functions
The Absolute Value Function
The Relation x - y[superscript 2] and Symmetry with Respect to the x-Axis
Even and Odd Functions
Vertical and Horizontal Shifts of Graphs
Vertical Shifts
Horizontal Shifts
Combinations of Vertical and Horizontal Shifts
Effects of Shifts on Domain and Range
Horizontal Shifts Applied to Equations for Modeling
Stretching, Shrinking, and Reflecting Graphs
Vertical Stretching
Vertical Shrinking
Horizontal Stretching and Shrinking
Reflecting across an Axis
Combining Transformations of Graphs
Reviewing Basic Concepts (Sections 2.1-2.3)
Absolute Value Functions: Graphs, Equations, Inequalities, and Applications
The Graph of y = [vertical bar]f(x)[vertical bar]
Properties of Absolute Value
Equations and Inequalities Involving Absolute Value
An Application Involving Absolute Value
Piecewise-Defined Functions
Graphing Piecewise-Defined Functions
The Greatest Integer Function
Applications of Piecewise-Defined Functions
Operations and Composition
Operations on Functions
The Difference Quotient
Composition of Functions
Applications of Operations and Composition
Reviewing Basic Concepts (Sections 2.4-2.6)
Chapter 2 Summary
Chapter 2 Review Exercises
Chapter 2 Test
Chapter 2 Project: Modeling the Movement of a Cold Front
Polynomial Functions
Complex Numbers
The Number i
Operations with Complex Numbers
Quadratic Functions and Graphs
Completing the Square
Graphs of Quadratic Functions
Vertex Formula
Extreme Values
Applications and Quadratic Models
Quadratic Equations and Inequalities
Zero-Product Property
Solving x[superscript 2] = k
Quadratic Formula and the Discriminant
Solving Quadratic Equations
Solving Quadratic Inequalities
Formulas Involving Quadratics
Another Quadratic Model
Reviewing Basic Concepts (Sections 3.1-3.3)
Further Applications of Quadratic Functions and Models
Applications of Quadratic Functions
Quadratic Models
Higher-Degree Polynomial Functions and Graphs
Cubic Functions
Quartic Functions
Extrema
End Behavior
x-Intercepts (Real Zeros)
Comprehensive Graphs
Curve Fitting and Polynomial Models
Reviewing Basic Concepts (Sections 3.4 and 3.5)
Topics in the Theory of Polynomial Functions (I)
Intermediate Value Theorem
Division of Polynomials and Synthetic Division
Remainder and Factor Theorems
Topics in the Theory of Polynomial Functions (II)
Complex Zeros and the Fundamental Theorem of Algebra
Number of Zeros
Rational Zeros Theorem
Descartes' Rule of Signs
Boundedness Theorem
Polynomial Equations and Inequalities; Further Applications and Models
Polynomial Equations and Inequalities
Complex nth Roots
Applications and Polynomial Models
Reviewing Basic Concepts (Sections 3.6-3.8)
Chapter 3 Summary
Chapter 3 Review Exercises
Chapter 3 Test
Chapter 3 Project: Creating a Social Security Polynomial
Rational, Power, and Root Functions
Rational Functions and Graphs
The Reciprocal Function
The Rational Function Defined by f(x) = 1 / x[superscript 2]
More on Graphs of Rational Functions
Vertical and Horizontal Asymptotes
Graphing Techniques
Oblique Asymptotes
Graphs with Points of Discontinuity
Rational Equations, Inequalities, Applications, and Models
Solving Rational Equations and Inequalities
Applications and Models of Rational Functions
Inverse Variation
Combined and Joint Variation
Reviewing Basic Concepts (Sections 4.1-4.3)
Functions Defined by Powers and Roots
Power and Root Functions
Modeling Using Power Functions
Graphs of f(x) = [characters not reproducible]
Graphing Circles and Horizontal Parabolas Using Root Functions
Equations, Inequalities, and Applications Involving Root Functions
Equations and Inequalities
An Application of Root Functions
Reviewing Basic Concepts (Sections 4.4 and 4.5)
Chapter 4 Summary
Chapter 4 Review Exercises
Chapter 4 Test
Chapter 4 Project: How Rugged Is Your Coastline?
Inverse, Exponential, and Logarithmic Functions
Inverse Functions
Inverse Operations
One-to-One Functions
Inverse Functions and Their Graphs
Equations of Inverse Functions
An Application of Inverse Functions
Exponential Functions
Real-Number Exponents
Graphs of Exponential Functions
Exponential Equations (Type 1)
Compound Interest
The Number e and Continuous Compounding
An Application of Exponential Functions
Logarithms and Their Properties
Definition of Logarithm
Common Logarithms
Natural Logarithms
Properties of Logarithms
Change-of-Base Rule
Reviewing Basic Concepts (Sections 5.1-5.3)
Logarithmic Functions
Graphs of Logarithmic Functions
Applying Earlier Work to Logarithmic Functions
A Logarithmic Model
Exponential and Logarithmic Equations and Inequalities
Exponential Equations and Inequalities (Type 2)
Logarithmic Equations and Inequalities
Equations and Inequalities Involving Both Exponentials and Logarithms
Formulas Involving Exponentials and Logarithms
Reviewing Basic Concepts (Sections 5.4 and 5.5)
Further Applications and Modeling with Exponential and Logarithmic Functions
Physical Science Applications
Financial Applications
Biological and Medical Applications
Modeling Data with Exponential and Logarithmic Functions
Chapter 5 Summary
Chapter 5 Review Exercises
Chapter 5 Test
Chapter 5 Project: Modeling Motor Vehicle Sales in the United States (with a lesson about the careless use of mathematical models)
Analytic Geometry
Circles and Parabolas
Conic Sections
Equations and Graphs of Circles
Equations and Graphs of Parabolas
Translations of Parabolas
An Application of Parabolas
Ellipses and Hyperbolas
Equations and Graphs of Ellipses
Translations of Ellipses
An Application of Ellipses
Equations and Graphs of Hyperbolas
Translations of Hyperbolas
Reviewing Basic Concepts (Sections 6.1 and 6.2)
Summary of the Conic Sections
Characteristics
Identifying Conic Sections
Eccentricity
Parametric Equations
Graphs of Parametric Equations and Their Rectangular Equivalents
Alternative Forms of Parametric Equations
An Application of Parametric Equations
Reviewing Basic Concepts (Sections 6.3 and 6.4)
Chapter 6 Summary
Chapter 6 Review Exercises
Chapter 6 Test
Chapter 6 Project: Modeling the Path of a Bouncing Ball
Systems of Equations and Inequalities; Matrices
Systems of Equations
Linear Systems
Substitution Method
Elimination Method
Special Systems
Nonlinear Systems
Applications of Systems
Solution of Linear Systems in Three Variables
Geometric Considerations
Analyttic Solution of Systems in Three Variables
Applications of Systems
Curve Fitting Using a System
Solution of Linear Systems by Row Transformations
Matrix Row Transformations
Row Echelon Method
Reduced Row Echelon Method
Special Cases
An Application of Matrices
Reviewing Basic Concepts (Sections 7.1-7.3)
Matrix Properties and Operations
Terminology of Matrices
Operations on Matrices
Applying Matrix Algebra
Determinants and Cramer's Rule
Determinants of 2 x 2 Matrices
Determinants of Larger Matrices
Derivation of Cramer's Rule
Using Cramer's Rule to Solve Systems
Solution of Linear Systems by Matrix Inverses
Identity Matrices
Multiplicative Inverses of Square Matrices
Using Determinants to Find Inverses
Solving Linear Systems Using Inverse Matrices
Curve Fitting Using a System
Reviewing Basic Concepts (Sections 7.4-7.6)
Systems of Inequalities and Linear Programming
Solving Linear Inequalities
Solving Systems of Inequalities
Linear Programming
Partial Fractions
Decomposition of Rational Expressions
Distinct Linear Factors
Repeated Linear Factors
Distinct Linear and Quadratic Factors
Repeated Quadratic Factors
Reviewing Basic Concepts (Sections 7.7 and 7.8)
Chapter 7 Summary
Chapter 7 Review Exercises
Chapter 7 Test
Chapter 7 Project: Finding a Polynomial Whose Graph Passes through Any Number of Given Points
Trigonometric Functions and Applications
Angles and Their Measures
Basic Terminology
Degree Measure
Standard Position and Coterminal Angles
Radian Measure
Arc Lengths and Areas of Sectors
Angular and Linear Speed
Trigonometric Functions and Fundamental Identities
Trigonometric Functions
Quadrantal Angles
Reciprocal Identities
Signs and Ranges of Function Values
Pythagorean Identities
Quotient Identities
An Application of Trigonometric Functions
Reviewing Basic Concepts (Sections 8.1 and 8.2)
Evaluating Trigonometric Functions
Definitions of the Trigonometric Functions
Trigonometric Function Values of Special Angles
Cofunction Identities
Reference Angles
Special Angles as Reference Angles
Finding Function Values with a Calculator
Finding Angle Measures
Applications of Right Triangles
Significant Digits
Solving Triangles
Angles of Elevation or Depression
Bearing
Further Applications of Trigonometric Functions
Reviewing Basic Concepts (Sections 8.3 and 8.4)
The Circular Functions
Circular Functions
Applications of Circular Functions
Graphs of the Sine and Cosine Functions
Periodic Functions
Graph of the Sine Function
Graph of the Cosine Function
Graphing Techniques, Amplitude, and Period
Translations
Determining a Trigonometric Model Using Curve Fitting
Reviewing Basic Concepts (Sections 8.5 and 8.6)
Graphs of the Other Circular Functions
Graphs of the Cosecant and Secant Functions
Graphs of the Tangent and Cotangent Functions
Addition of Ordinates
Harmonic Motion
Simple Harmonic Motion
Damped Oscillatory Motion
Reviewing Basic Concepts (Sections 8.7 and 8.8)
Chapter 8 Summary
Chapter 8 Review Exercises
Chapter 8 Test
Chapter 8 Project: Modeling Sunset Times
Trigonometric Identities and Equations
Trigonometric Identities
Fundamental Identities
Using the Fundamental Identities
Verifying Identities
Sum and Difference Identities
Cosine Sum and Difference Identities
Sine and Tangent Sum and Difference Identities
Reviewing Basic Concepts (Sections 9.1 and 9.2)
Further Identities
Double-Number Identities
Product-to-Sum and Sum-to-Product Identities
Half-Number Identities
The Inverse Circular Functions
Review of Inverse Functions
Inverse Sine Function
Inverse Cosine Function
Inverse Tangent Function
Remaining Inverse Trigonometric Functions
Inverse Function Values
Reviewing Basic Concepts (Sections 9.3 and 9.4)
Trigonometric Equations and Inequalities (I)
Equations Solvable by Linear Methods
Equations Solvable by Factoring
Equations Solvable by the Quadratic Formula
Using Trigonometric Identities to Solve Equations
Trigonometric Equations and Inequalities (II)
Equations and Inequalities Involving Multiple-Number Identities
Equations and Inequalities Involving Half-Number Identities
An Application of Trigonometric Equations
Reviewing Basic Concepts (Sections 9.5 and 9.6)
Chapter 9 Summary
Chapter 9 Review Exercises
Chapter 9 Test
Chapter 9 Project: Modeling a Damped Pendulum
Applications of Trigonometry; Vectors
The Law of Sines
Congruency and Oblique Triangles
Derivation of the Law of Sines
Applications of Triangles
Ambiguous Case
The Law of Cosines and Area Formulas
Derivation of the Law of Cosines
Applications of Triangles
Area Formulas
Vectors and Their Applications
Basic Terminology
Algebraic Interpretation of Vectors
Operations with Vectors
Dot Product and the Angle between Vectors
Applications of Vectors
Reviewing Basic Concepts (Sections 10.1-10.3)
Trigonometric (Polar) Form of Complex Numbers
The Complex Plane and Vector Representation
Trigonometric (Polar) Form
Products of Complex Numbers in Trigonometric Form
Quotients of Complex Numbers in Trigonometric Form
Powers and Roots of Complex Numbers
Powers of Complex Numbers (De Moivre's Theorem)
Roots of Complex Numbers
Reviewing Basic Concepts (Sections 10.4 and 10.5)
Polar Equations and Graphs
Polar Coordinate System
Graphs of Polar Equations
Classifying Polar Equations
Converting Equations
More Parametric Equations
Parametric Equations with Trigonometric Functions
The Cycloid
Applications of Parametric Equations
Reviewing Basic Concepts (Sections 10.6 and 10.7)
Chapter 10 Summary
Chapter 10 Review Exercises
Chapter 10 Test
Chapter 10 Project: When Is a Circle Really a Polygon?
Further Topics in Algebra
Sequences and Series
Sequences
Series and Summation Notation
Summation Properties
Arithmetic Sequences and Series
Arithmetic Sequences
Arithmetic Series
Geometric Sequences and Series
Geometric Sequences
Geometric Series
Infinite Geometric Series
Annuities
Reviewing Basic Concepts (Sections 11.1-11.3)
The Binomial Theorem
A Binomial Expansion Pattern
Pascal's Triangle
n-Factorial
Binomial Coefficients
The Binomial Theorem
rth Term of a Binomial Expansion
Mathematical Induction
Proof by Mathematical Induction
Proving Statements
Generalized Principle of Mathematical Induction
Proof of the Binomial Theorem
Reviewing Basic Concepts (Sections 11.4 and 11.5)
Counting Theory
Fundamental Principle of Counting
Permutations
Combinations
Distinguishing between Permutations and Combinations
Probability
Basic Concepts
Complements and Venn Diagrams
Odds
Union of Two Events
Binomial Probability
Reviewing Basic Concepts (Sections 11.6 and 11.7)
Chapter 11 Summary
Chapter 11 Review Exercises
Chapter 11 Test
Chapter 11 Project: Using Experimental Probabilities to Simulate Family Makeup
Reference: Basic Algebraic Concepts
Review of Exponents and Polynomials
Rules for Exponents
Terminology for Polynomials
Adding and Subtracting Polynomials
Multiplying Polynomials
Review of Factoring
Factoring Out the Greatest Common Factor
Factoring by Grouping
Factoring Trinomials
Factoring Special Products
Factoring by Substitution
Review of Rational Expressions
Domain of a Rational Expression
Lowest Terms of a Rational Expression
Multipling and Dividing Rational Expressions
Adding and Subtracting Rational Expressions
Complex Fractions
Review of Negative and Rational Exponents
Negative Exponents and the Quotient Rule
Rational Exponents
Review of Radicals
Radical Notation
Rules for Radicals
Simplifying Radicals
Operations with Radicals
Rationalizing Denominators
Chapter R Test
Geometry Formulas
Deciding Which Model Best Fits a Set of Data
Vectors in Space
Polar Form of Conic Sections
Rotation of Axes
Answers to Selected Exercises
Index of Applications
Index

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