Elementary and Intermediate Algebra, 4th Edition

Cover
Title Page
Copyright
ISBN-13: 9780073384351
Contents
Applications Index
Chapter 1 Real Numbers and Their Properties
1.1 The Real Numbers
1 The Integers
2 The Rational Numbers
3 The Number Line
4 The Real Numbers
5 Intervals of Real Numbers
6 Absolute Value
1.2 Fractions
1 Equivalent Fractions
2 Multiplying Fractions
3 Unit Conversion
4 Dividing Fractions
5 Adding and Subtracting Fractions
6 Fractions,Decimals, and Percents
7 Applications
1.3 Addition and Subtraction of Real Numbers
1 Addition of Two Negative Numbers
2 Addition of Numbers with Unlike Signs
3 Subtraction of Signed Numbers
4 Applications
1.4 Multiplication and Division of Real Numbers
1 Multiplication of Real Numbers
2 Division of Real Numbers
3 Division by Zero
Mid-Chapter Quiz
1.5 Exponential Expressions and the Order of Operations
1 Arithmetic Expressions
2 Exponential Expressions
3 The Order of Operations
4 Applications
1.6 Algebraic Expressions
1 Identifying Algebraic Expressions
2 Translating Algebraic Expressions
3 Evaluating Algebraic Expressions
4 Equations
5 Applications
1.7 Properties of the Real Numbers
1 The Commutative Properties
2 The Associative Properties
3 The Distributive Property
4 The Identity Properties
5 The Inverse Properties
6 Identifying the Properties
1.8 Using the Properties to Simplify Expressions
1 Using the Properties in Computation
2 Combining Like Terms
3 Products and Quotients
4 Removing Parentheses
5 Applications
Chapter 1 Wrap-Up
Summary
Enriching Your Mathematical Word Power
Review Exercises
Chapter 1 Test
Critical Thinking
Chapter 2 Linear Equations and Inequalities in One Variable
2.1 The Addition and Multiplication Properties of Equality
1 The Addition Property of Equality
2 The Multiplication Property of Equality
3 Variables on Both Sides
4 Applications
2.2 Solving General Linear Equations
1 Equations of the Form ax + b = 0
2 Equations of the Form ax + b = cx + d
3 Equations with Parentheses
4 Applications
2.3 More Equations
1 Equations Involving Fractions
2 Equations Involving Decimals
3 Simplifying the Process
4 Identities, Conditional Equations, and Inconsistent Equations
5 Applications
2.4 Formulas and Functions
1 Solving for a Variable
2 The Language of Functions
3 Finding the Value of a Variable
4 Applications
Mid-Chapter Quiz
2.5 Translating Verbal Expressions into Algebraic Expressions
1 Writing Algebraic Expressions
2 Pairs of Numbers
3 Consecutive Integers
4 Using Formulas
5 Writing Equations
2.6 Number, Geometric, and Uniform Motion Applications
1 Number Problems
2 General Strategy for Solving Verbal Problems
3 Geometric Problems
4 Uniform Motion Problems
2.7 Discount, Investment, and Mixture Applications
1 Discount Problems
2 Commission Problems
3 Investment Problems
4 Mixture Problems
2.8 Inequalities
1 Inequalities
2 Graphing Inequalities
3 Graphing Compound Inequalities
4 Checking Inequalities
5 Writing Inequalities
2.9 Solving Inequalities and Applications
1 Rules for Inequalities
2 Solving Inequalities
3 Applications
Chapter 2 Wrap-Up
Summary
Enriching Your Mathematical Word Power
Review Exercises
Chapter 2 Test
Making Connections: A Review of Chapters 1–2
Critical Thinking
Chapter 3 Linear Equations in Two Variables and Their Graphs
3.1 Graphing Lines in the Coordinate Plane 170
1 Graphing Ordered Pairs
2 Ordered Pairs as Solutions to Equations
3 Graphing a Linear Equation in Two Variables
4 Graphing a Line Using Intercepts
5 Function Notation and Applications
3.2 Slope
1 Slope
2 Slope Using Coordinates
3 Graphing a Line Given a Point and Slope
4 Parallel Lines
5 Perpendicular Lines
6 Applications
3.3 Equations of Lines in Slope-Intercept Form
1 Slope-Intercept Form
2 Standard Form
3 Using Slope-Intercept Form for Graphing
4 Writing the Equation for a Line
5 Applications
Mid-Chapter Quiz
3.4 The Point-Slope Form
1 Point-Slope Form
2 Parallel Lines
3 Perpendicular Lines
4 Applications
3.5 Variation
1 Direct, Inverse, and Joint Variation
2 Finding the Variation Constant
3 Applications
3.6 Graphing Linear Inequalities in Two Variables
1 Linear Inequalities
2 Graphing a Linear Inequality
3 The Test-Point Method
4 Applications
Chapter 3 Wrap-Up
Summary
Enriching Your Mathematical Word Power
Review Exercises
Chapter 3 Test
Making Connections: A Review of Chapters 1–3
Critical Thinking
Chapter 4 Exponents and Polynomials
4.1 The Rules of Exponents
1 The Product Rule for Exponents
2 Zero Exponent
3 The Quotient Rule for Exponents
4 The Power of a Power Rule
5 The Power of a Product Rule
6 The Power of a Quotient Rule
7 The Amount Formula
4.2 Negative Exponents
1 Negative Integral Exponents
2 The Rules for Integral Exponents
3 The Present Value Formula
4.3 Scientific Notation
1 Converting Scientific to Standard Notation
2 Converting Standard to Scientific Notation
3 Combining Numbers and Words
4 Computations with Scientific Notation
5 Applications
4.4 Addition and Subtraction of Polynomials
1 Polynomials
2 Evaluating Polynomials
3 Addition of Polynomials
4 Subtraction of Polynomials
5 Applications
Mid-Chapter Quiz
4.5 Multiplication of Polynomials
1 Multiplying Monomials
2 Multiplying Polynomials
3 The Additive Inverse of a Polynomial
4 Applications
4.6 Multiplication of Binomials
1 The FOIL Method
2 Multiplying Binomials Quickly
3 Applications
4.7 Special Products
1 The Square of a Sum or Difference
2 Product of a Sum and a Difference
3 Higher Powers of Binomials
4 Applications
4.8 Division of Polynomials
1 Dividing Monomials
2 Dividing a Polynomial by a Monomial
3 Dividing a Polynomial by a Binomial
Chapter 4 Wrap-Up
Summary
Enriching Your Mathematical Word Power
Review Exercises
Chapter 4 Test
Making Connections: A Review of Chapters 1–4
Critical Thinking
Chapter 5 Factoring
5.1 Factoring Out Common Factors
1 Prime Factorization of Integers
2 Greatest Common Factor
3 Greatest Common Factor for Monomials
4 Factoring Out the Greatest Common Factor
5 Factoring Out the Opposite of the GCF
6 Applications
5.2 Special Products and Grouping
1 Factoring by Grouping
2 Factoring a Difference of Two Squares
3 Factoring a Perfect Square Trinomial
4 Factoring Completely
5.3 Factoring the Trinomial ax[Sup(2)] + bx + c with a = 1
1 Factoring ax[Sup(2)] + bx + c with a = 1
2 Factoring with Two Variables
3 Factoring Completely
Mid-Chapter Quiz
5.4 Factoring the Trinomial ax[Sup(2)] + bx + c with a ≠ 1
1 The ac Method
2 Trial and Error
3 Factoring Completely
5.5 Difference and Sum of Cubes and a Strategy
1 Factoring a Difference or Sum of Two Cubes
2 Factoring a Difference of Two Fourth Powers
3 The Factoring Strategy
5.6 Solving Quadratic Equations by Factoring
1 The Zero Factor Property
2 Fractions and Decimals
3 Applications
Chapter 5 Wrap-Up
Summary
Enriching Your Mathematical Word Power
Review Exercises
Chapter 5 Test
Making Connections: A Review of Chapters 1–5
Critical Thinking
Chapter 6 Rational Expressions
6.1 Reducing Rational Expressions
1 Rational Expressions and Functions
2 Reducing to Lowest Terms
3 Reducing with the Quotient Rule for Exponents
4 Dividing a - b by b - a
5 Factoring Out the Opposite of a Common Factor
6 Writing Rational Expressions
6.2 Multiplication and Division
1 Multiplication of Rational Numbers
2 Multiplication of Rational Expressions
3 Division of Rational Numbers
4 Division of Rational Expressions
5 Applications
6.3 Finding the Least Common Denominator
1 Building Up the Denominator
2 Finding the Least Common Denominator
3 Converting to the LCD
6.4 Addition and Subtraction
1 Addition and Subtraction of Rational Numbers
2 Addition and Subtraction of Rational Expressions
3 Applications
Mid-Chapter Quiz
6.5 Complex Fractions
1 Complex Fractions
2 Using the LCD to Simplify Complex Fractions
3 Applications
6.6 Solving Equations with Rational Expressions
1 Equations with Rational Expressions
2 Extraneous Solutions
6.7 Applications of Ratios and Proportions
1 Ratios
2 Proportions
6.8 Applications of Rational Expressions
1 Formulas
2 Uniform Motion Problems
3 Work Problems
4 More Rate Problems
Chapter 6 Wrap-Up
Summary
Enriching Your Mathematical Word Power
Review Exercises
Chapter 6 Test
Making Connections: A Review of Chapters 1–6
Critical Thinking
Chapter 7 Systems of Linear Equations
7.1 The Graphing Method
1 Solving a System by Graphing
2 Types of Systems
3 Applications
7.2 The Substitution Method
1 Solving a System by Substitution
2 Dependent and Inconsistent Systems
3 Applications
Mid-Chapter Quiz
7.3 The Addition Method
1 The Addition Method
2 Equations Involving Fractions or Decimals
3 Applications
7.4 Systems of Linear Equations in Three Variables
1 Definition
2 Solving a System by Elimination
3 Dependent and Inconsistent Systems
4 Applications
Chapter 7 Wrap-Up
Summary
Enriching Your Mathematical Word Power
Review Exercises
Chapter 7 Test
Making Connections: A Review of Chapters 1–7
Critical Thinking
Chapter 8 More on Inequalities
8.1 Compound Inequalities in One Variable
1 Compound Inequalities
2 Graphing the Solution Set
3 Applications
8.2 Absolute Value Equations and Inequalities
1 Absolute Value Equations
2 Absolute Value Inequalities
3 All or Nothing
4 Applications
Mid-Chapter Quiz
8.3 Compound Inequalities in Two Variables
1 Satisfying a Compound Inequality
2 Graphing Compound Inequalities
3 Absolute Value Inequalities
4 Inequalities with No Solution
5 Applications
8.4 Linear Programming
1 Graphing the Constraints
2 Maximizing or Minimizing
Chapter 8 Wrap-Up
Summary
Enriching Your Mathematical Word Power
Review Exercises
Chapter 8 Test
Making Connections: A Review of Chapters 1–8
Critical Thinking
Chapter 9 Radicals and Rational Exponents
9.1 Radicals
1 Roots
2 Roots and Variables
3 Product Rule for Radicals
4 Quotient Rule for Radicals
5 Domain of a Radical Expression or Function
9.2 Rational Exponents
1 Rational Exponents
2 Using the Rules of Exponents
3 Simplifying Expressions Involving Variables
9.3 Adding, Subtracting, and Multiplying Radicals
1 Adding and Subtracting Radicals
2 Multiplying Radicals
3 Conjugates
4 Multiplying Radicals with Different Indices
Mid-Chapter Quiz
9.4 Quotients, Powers, and Rationalizing Denominators
1 Rationalizing the Denominator
2 Simplifying Radicals
3 Dividing Radicals
4 Rationalizing Denominators Using Conjugates
5 Powers of Radical Expressions
9.5 Solving Equations with Radicals and Exponents
1 The Odd-Root Property
2 The Even-Root Property
3 Equations Involving Radicals
4 Equations Involving Rational Exponents
5 Applications
9.6 Complex Numbers
1 Definition
2 Addition, Subtraction, and Multiplication
3 Division of Complex Numbers
4 Square Roots of Negative Numbers
5 Imaginary Solutions to Equations
Chapter 9 Wrap-Up
Summary
Enriching Your Mathematical Word Power
Review Exercises
Chapter 9 Test
Making Connections: A Review of Chapters 1–9
Critical Thinking
Chapter 10 Quadratic Equations, Functions, and Inequalities
10.1 Factoring and Completing the Square
1 Review of Factoring
2 Review of the Even-Root Property
3 Completing the Square
4 Radicals and Rational Expressions
5 Imaginary Solutions
10.2 The Quadratic Formula
1 Developing the Formula
2 Using the Formula
3 Number of Solutions
4 Applications
10.3 More on Quadratic Equations
1 Writing a Quadratic Equation with Given Solutions
2 Using the Discriminant in Factoring
3 Equations Quadratic in Form
4 Applications
Mid-Chapter Quiz
10.4 Graphing Quadratic Functions
1 Finding Ordered Pairs
2 Graphing Quadratic Functions
3 The Vertex and Intercepts
4 Applications
10.5 Quadratic Inequalities
1 Solving Quadratic Inequalities Graphically
2 Solving Quadratic Inequalities with the Test-Point Method
3 Applications
Chapter 10 Wrap-Up
Summary
Enriching Your Mathematical Word Power
Review Exercises
Chapter 10 Test
Making Connections: A Review of Chapters 1–10
Critical Thinking
Chapter 11 Functions
11.1 Functions and Relations
1 The Concept of a Function
2 Functions Expressed by Formulas
3 Functions Expressed by Tables
4 Functions Expressed by Ordered Pairs
5 The Vertical-Line Test
6 Domain and Range
7 Function Notation
11.2 Graphs of Functions and Relations
1 Linear and Constant Functions
2 Absolute Value Functions
3 Quadratic Functions
4 Square-Root Functions
5 Piecewise Functions
6 Graphing Relations
11.3 Transformations of Graphs
1 Horizontal Translation
2 Stretching and Shrinking
3 Reflecting
4 Vertical Translation
5 Multiple Transformations
Mid-Chapter Quiz
11.4 Graphs of Polynomial Functions
1 Cubic Functions
2 Quartic Functions
3 Symmetry
4 Behavior at the x-Intercepts
5 Transformations
6 Solving Polynomial Inequalities
11.5 Graphs of Rational Functions
1 Rational Functions
2 Asymptotes
3 Sketching the Graphs
4 Rational Inequalities
11.6 Combining Functions
1 Basic Operations with Functions
2 Composition
11.7 Inverse Functions
1 Inverse of a Function
2 Identifying Inverse Functions
3 Switch-and-Solve Strategy
4 Even Roots or Even Powers
5 Graphs of f and f 1
Chapter 11 Wrap-Up
Summary
Enriching Your Mathematical Word Power
Review Exercises
Chapter 11 Test
Making Connections: A Review of Chapters 1–11
Critical Thinking
Chapter 12 Exponential and Logarithmic Functions
12.1 Exponential Functions and Their Applications
1 Exponential Functions
2 Graphing Exponential Functions
3 Transformations of Exponential Functions
4 Exponential Equations
5 Applications
12.2 Logarithmic Functions and Their Applications
1 Logarithmic Functions
2 Graphing Logarithmic Functions
3 Logarithmic Equations
4 Applications
Mid-Chapter Quiz
12.3 Properties of Logarithms
1 The Inverse Properties
2 The Product Rule for Logarithms
3 The Quotient Rule for Logarithms
4 The Power Rule for Logarithms
5 Using the Properties
12.4 Solving Equations and Applications
1 Logarithmic Equations
2 Exponential Equations
3 Changing the Base
4 Strategy for Solving Equations
5 Applications
Chapter 12 Wrap-Up
Summary
Enriching Your Mathematical Word Power
Review Exercises
Chapter 12 Test
Making Connections: A Review of Chapters 1–12
Critical Thinking
Chapter 13 Nonlinear Systems and the Conic Sections
13.1 Nonlinear Systems of Equations
1 Solving by Elimination
2 Applications
13.2 The Parabola
1 The Distance and Midpoint Formulas
2 The Parabola
3 Changing Forms
4 Parabolas Opening to the Right or Left
13.3 The Circle
1 The Equation of a Circle
2 Equations Not in Standard Form
3 Systems of Equations
Mid-Chapter Quiz
13.4 The Ellipse and Hyperbola
1 The Ellipse
2 The Hyperbola
13.5 Second-Degree Inequalities
1 Graphing a Second-Degree Inequality
2 Systems of Inequalities
Chapter 13 Wrap-Up
Summary
Enriching Your Mathematical Word Power
Review Exercises
Chapter 13 Test
Making Connections: A Review of Chapters 1–13
Critical Thinking
Chapter 14 Sequences and Series (Available online at www.mhhe.com/dugopolski)
14.1 Sequences
1 Sequences
2 Finding a Formula for the nth Term
14.2 Series
1 Summation Notation
2 Series
3 Changing the Index
14.3 Arithmetic Sequences and Series
1 Arithmetic Sequences
2 Arithmetic Series
Mid-Chapter Quiz
14.4 Geometric Sequences and Series
1 Geometric Sequences
2 Finite Geometric Series
3 Infinite Geometric Series
4 Applications
14.5 Binomial Expansions
1 Some Examples
2 Obtaining the Coefficients
3 The Binomial Theorem
Chapter 14 Wrap-Up
Summary
Enriching Your Mathematical Word Power
Review Exercises
Chapter 14 Test
Making Connections: A Review of Chapters 1–14
Critical Thinking
Appendix
A: Geometry Review Exercises
B: Sets
C: Chapters 1–6 Diagnostic Test A-8
D: Chapters 1–6 Review
Answers to Selected Exercises
Index