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College Algebra with Modeling and Visualization

ISBN: 9780321279088 | 0321279085
Edition: 3rd
Format: Hardcover
Publisher: Addison Wesley
Pub. Date: 1/1/2006

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SummaryTable of Contents
Gary Rockswold focuses on teaching algebra in context, answering the question, "Why am I learning this?" and ultimately motivating the reader to succeed. Introduction to Functions and Graphs. Linear Functions and Equations. Quadratic Functions and Equations. Nonlinear Functions and Equations. Exponential and Logarithmic Functions. Systems of Equations and Inequalities. Conic Sections. Further Topics in Algebra. Basic Concepts From Algebra and Geometry. For all readers interested in college algebra.
Prefacexiii
Introduction To Functions and Graphs
1(71)
Numbers, Data, and Problem Solving
2(12)
... MORE
Sets of Numbers
Scientific Notation
Problem Solving
Visualization of Data
14(15)
One-Variable Data
Two-Variable Data
The Distance Formula
The Midpoint Formula
Graphing with a Calculator (Optional)
Checking Basic Concepts for Sections 1.1 and 1.2
29(1)
Functions and Their Representations
29(17)
Basic Concepts
Representations of Functions
Formal Definition of a Function
Graphing Calculators and Functions (Optional)
Identifying Functions
Types of Functions and Their Rates of Change
46(26)
Constant Functions
Linear Functions
Slope as a Rate of Change
Nonlinear Functions
Average Rate of Change
The Difference Quotient
Checking Basic Concepts for Sections 1.3 and 1.4
62(1)
Summary
62(4)
Review Exercises
66(4)
Extended and Discovery Exercises
70(2)
Linear Functions and Equations
72(99)
Linear Functions and Models
73(14)
Exact and Approximate Models
Representations of Linear Functions
Modeling with Linear Functions
Linear Regression (Optional)
Equations of Lines
87(19)
Forms for Equations of Lines
Determining Intercepts
Horizontal, Vertical, Parallel, and Perpendicular Lines
Modeling Data (Optional)
Interpolation and Extrapolation
Direct Variation
Checking Basic Concepts for Sections 2.1 and 2.2
106(1)
Linear Equations
106(17)
Equations
Symbolic Solutions
Graphical and Numerical Solutions
Problem-Solving Strategies
Linear Inequalities
123(17)
Inequalities
Interval Notation
Techniques for Solving Inequalities
Compound Inequalities
Checking Basic Concepts for Sections 2.3 and 2.4
139(1)
Piecewise-Defined Functions
140(31)
Evaluating and Graphing Piecewise-Defined Functions
The Greatest Integer Function
The Absolute Value Function
Equations and Inequalities Involving Absolute Values
Checking Basic Concepts for Section 2.5
158(1)
Summary
158(4)
Review Exercises
162(4)
Extended and Discovery Exercises
166(1)
Cumulative Review Exercises
167(4)
Quadratic Functions and Equations
171(70)
Quadratic Functions and Models
172(17)
Basic Concepts
Completing the Square and the Vertex Formula
Applications and Models
Quadratic Regression (Optional)
Quadratic Equations and Problem Solving
189(17)
Basic Concepts
Solving Quadratic Equations
Problem Solving
Checking Basic Concepts for Sections 3.1 and 3.2
205(1)
Quadratic Inequalities
206(10)
Graphical Solutions
Symbolic Solutions
Transformations of Graphs
216(25)
Vertical and Horizontal Translations
Stretching and Shrinking
Reflection of Graphs
Combining Transformations
Modeling with Transformations (Optional)
Checking Basic Concepts for Sections 3.3 and 3.4
233(1)
Summary
234(3)
Review Exercises
237(2)
Extended and Discovery Exercises
239(2)
Nonlinear Functions and Equations
241(122)
Nonlinear Functions and Their Graphs
242(15)
Polynomial Functions
Increasing and Decreasing Functions
Extrema of Nonlinear Functions
Symmetry
Polynomial Functions and Models
257(17)
Graphs of Polynomial Functions
Piecewise-Defined Polynomial Functions
Polynomial Regression (Optional)
Checking Basic Concepts for Sections 4.1 and 4.2
273(1)
Real Zeros of Polynomial Functions
274(19)
Division of Polynomials
Factoring Polynomials
Graphs and Multiple Zeros
Rational Zeros
Polynomial Equations
The Fundamental Theorem of Algebra
293(12)
Complex Numbers
Quadratic Equations with Complex Solutions
Fundamental Theorem of Algebra
Polynomial Equations with Complex Solutions
Checking Basic Concepts for Sections 4.3 and 4.4
305(1)
Rational Functions and Models
305(20)
Rational Functions
Vertical Asymptotes
Horizontal Asymptotes
Identifying Asymptotes
Rational Equations
Variation
Polynomial and Rational Inequalities
325(9)
Polynomial Inequalities
Rational Inequalities
Checking Basic Concepts for Sections 4.5 and 4.6
334(1)
Power Functions and Radical Equations
334(29)
Rational Exponents and Radical Notation
Power Functions and Models
Equations Involving Rational Exponents
Equations Involving Radicals
Power Regression (Optional)
Checking Basic Concepts for Section 4.7
346(1)
Summary
347(5)
Review Exercises
352(5)
Extended and Discovery Exercises
357(1)
Cumulative Review Exercises
358(5)
Exponential and Logarithmic Functions
363(111)
Combining Functions
364(18)
Arithmetic Operations on Functions
Composition of Functions
Inverse Functions and Their Representations
382(17)
Inverse Operations
One-to-One Functions
Symbolic Representations of Inverse Functions
Other Representations of Inverse Functions
Checking Basic Concepts for Sections 5.1 and 5.2
399(1)
Exponential Functions and Models
399(20)
Linear and Exponential Growth
Exponential Models
Compound Interest
The Natural Exponential Function
Logarithmic Functions and Models
419(17)
The Common Logarithmic Function
Basic Equations
Logarithms with Other Bases
General Logarithmic Equations
Checking Basic Concepts for Sections 5.3 and 5.4
435(1)
Properties of Logarithms
436(8)
Basic Properties of Logarithms
Change of Base Formula
Exponential and Logarithmic Equations
444(13)
Exponential Equations
Logarithmic Equations
Checking Basic Concepts for Sections 5.5 and 5.6
457(1)
Constructing Nonlinear Models
457(17)
Exponential Model
Logarithmic Model
Logistic Model
Checking Basic Concepts for Section 5.7
464(1)
Summary
464(4)
Review Exercises
468(4)
Extended and Discovery Exercises
472(2)
Systems of Equations and Inequalities
474(110)
Functions and Equations in Two Variables
475(15)
Functions of Two Variables
Systems of Equations
The Method of Substitution
Graphical and Numerical Methods
Joint Variation
Systems of Equations and Inequalities in Two Variables
490(18)
Types of Linear Systems in Two Variables
The Elimination Method
Systems of Linear and Nonlinear Inequalities
Linear Programming
Checking Basic Concepts for Sections 6.1 and 6.2
508(1)
Systems of Linear Equations in Three Variables
508(8)
Basic Concepts
Solving with Elimination and Substitution
Systems of Linear and Nonlinear Inequalities
Systems with Infinitely Many Solutions
Solutions to Linear Systems Using Matrices
516(17)
Representing Systems of Linear Equations with Matrices
Row-Echelon Form
Gaussian Elimination
Solving Systems of Linear Equations with Technology (Optional)
Checking Basic Concepts for Sections 6.3 and 6.4
532(1)
Properties and Applications of Matrices
533(14)
Matrix Notation
Sums, Differences, and Scalar Multiples of Matrices
Matrix Products
Technology and Matrices (Optional)
Inverses of Matrices
547(14)
Matrix Inverses
Finding Inverses Symbolically
Representing Linear Systems with Matrix Equations
Solving Linear Systems with Inverses
Checking Basic Concepts for Sections 6.5 and 6.6
560(1)
Determinants
561(23)
Definition and Calculation of Determinants
Area of Regions
Cramer's Rule
Limitations on the Method of Cofactors and Cramer's Rule
Checking Basic Concepts for Section 6.7
569(1)
Summary
570(4)
Review Exercises
574(3)
Extended and Discovery Exercises
577(2)
Cumulative Review Exercises
579(5)
Conic Sections
584(43)
Parabolas
585(10)
Equations and Graphs of Parabolas
Reflective Property of Parabolas
Translations of Parabolas
Ellipses
595(15)
Equations and Graphs of Ellipses
Reflective Property of Ellipses
Translations of Ellipses
Circles
Solving Systems of Nonlinear Equations and Inequalities
Checking Basic Concepts for Sections 7.1 and 7.2
610(1)
Hyperbolas
610(17)
Equations and Graphs of Hyperbolas
Reflective Property of Hyperbolas
Translations of Hyperbolas
Solving Systems of Nonlinear Equations
Checking Basic Concepts for Section 7.3
621(1)
Summary
622(2)
Review Exercises
624(2)
Extended and Discovery Exercises
626(1)
Further Topics in Algebra
627
Sequences
628(14)
Basic Concepts
Representations of Sequences
Arithmetic Sequences
Geometric Sequences
Series
642(16)
Basic Concepts
Arithmetic Series
Geometric Series
Summation Notation
Checking Basic Concepts for Sections 8.1 and 8.2
658(1)
Counting
658(11)
Fundamental Counting Principle
Permutations
Combinations
The Binomial Theorem
669(6)
Derivation of the Binomial Theorem
Pascal's Triangle
Checking Basic Concepts for Sections 8.3 and 8.4
674(1)
Mathematical Induction
675(6)
Mathematical Induction
Proving Statements
Generalized Principle of Mathematical Induction
Probability
681
Definition of Probability
Compound Events
Independent and Dependent Events
Checking Basic Concepts for Sections 8.5 and 8.6
694(1)
Summary
694(4)
Review Exercises
698(2)
Extended and Discovery Exercises
700(1)
Cumulative Review Exercises
701
Reference: Basic Concepts from Algebra and Geometry
1(1)
Formulas from Geometry
1(9)
Geometric Shapes in a Plane
The Pythagorean Theorem
Three-Dimensional Objects
Similar Triangles
A Summary of Geometric Formulas
Circles
10(3)
Equations and Graphs of Circles
Finding the Center and Radius of a Circle
Integer Exponents
13(7)
Bases and Positive Exponents
Zero and Negative Exponents
Product, Quotient, and Power Rules
Polynomial Expressions
20(7)
Addition and Subtraction of Monomials
Addition and Subtraction of Polynomials
Distributive Properties
Multiplying Polynomials
Some Special Products
Factoring Polynomials
27(11)
Common Factors
Factoring by Grouping
Factoring x2 + bx + c
Factoring Trinomials by Grouping
Factoring Trinomials with FOIL
Difference of Two Squares
Perfect Square Trinomials
Sum and Difference of Two Cubes
Rational Expressions
38(10)
Simplifying Rational Expressions
Multiplication and Division of Rational Expressions
Least Common Multiples
Common Denominators
Addition and Subtraction of Rational Expressions
Clearing Fractions
Complex Fractions
Radical Notation and Rational Exponents
48(7)
Radical Notation
Rational Exponents
Properties of Rational Exponents
Radical Expressions
55
Product Rule for Radical Expressions
Quotient Rule for Radical Expressions
Addition and Subtraction
Multiplication
Rationalizing the Denominator
Appendix A: A Library of Functions1(3)
Appendix B: Using the Graphing Calculator4
Bibliography1(1)
Answers to Selected Exercises1(1)
Index of Applications1(5)
Index6

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