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Concepts and Vocabulary
by J. S. Ratti, Marcus S. McWaters, Leslaw Skrzypek
College Algebra, 4th Edition
MyLab Math Online Course for College Algebra by Ratti, McWaters, Skrzypek (access code required)
Connect the Concepts and Relate the Math
College Algebra
College Algebra
Foreword
Contents
Preface
Key Content Changes
Features
Get the Most Out of MyLab Math
Resources for Success
Dedication
Chapter P Basic Concepts of Algebra
Topics
Section P.1 The Real Numbers and Their Properties
Before Starting This Section, Review From Your Previous Mathematics Texts
Objectives
Classifying Numbers
Equality of Numbers
Classifying Sets of Numbers
Rational Numbers
Solution
Practice Problem 1
Irrational Numbers
Solution
Practice Problem 2
Integer Exponents
Solution
Practice Problem 3
The Real Number Line
Inequalities
Solution
Practice Problem 4
Sets
Definition of Union and Intersection
Solution
Practice Problem 5
Intervals
Solution
Practice Problem 6
Absolute Value
Solution
Practice Problem 7
Distance Between Two Points on a Real Number Line
Solution
Practice Problem 8
Order of Operations
Solution
Practice Problem 9
Properties of the Real Numbers
Subtraction and Division of Real Numbers
Solution
Practice Problem 10
Algebraic Expressions
Solution
Practice Problem 11
Solution
Practice Problem 12
Section P.1 Exercises
Concepts and Vocabulary
Building Skills
Applying the Concepts
Beyond the Basics
Getting Ready for the Next Section
Section P.2 Integer Exponents and Scientific Notation
Before Starting This Section, Review
Objectives
Integer Exponents
Solution
Practice Problem 1
Rules of Exponents
Solution
Practice Problem 2
Solution
Practice Problem 3
Solution
Practice Problem 4
Solution
Practice Problem 5
Solution
Practice Problem 6
Simplifying Exponential Expressions
Solution
Practice Problem 7
Scientific Notation
Solution
Practice Problem 8
Practice Problem 9
Section P.2 Exercises
Concepts and Vocabulary
Building Skills
Applying the Concepts
Beyond the Basics
Getting Ready for the Next Section
Section P.3 Polynomials
Before Starting This Section, Review
Objectives
Polynomial Vocabulary
Solution
Practice Problem 1
Adding and Subtracting Polynomials
Practice Problem 2
Practice Problem 3
Multiplying Polynomials
Practice Problem 4
Practice Problem 5
Special Products
Practice Problem 6
Squaring a Binomial Sum or Difference
Solution
Practice Problem 7
The Product of the Sum and Difference of Terms
Solution
Practice Problem 8
Solution
Practice Problem 9
Section P.3 Exercises
Concepts and Vocabulary
Building Skills
Applying the Concepts
Beyond the Basics
Getting Ready for the Next Section
Section P.4 Factoring Polynomials
Before Starting This Section, Review
Objectives
The Greatest Common Monomial Factor
Factoring Out a Monomial
Solution
Practice Problem 1
Factoring Trinomials of the Form x2+Bx+C
Solution
Practice Problem 2
Factoring Formulas
Perfect-Square Trinomials
Solution
Practice Problem 3
Difference of Squares
Solution
Practice Problem 4
Solution
Practice Problem 5
Difference and Sum of Cubes
Solution
Practice Problem 6
Solution
Practice Problem 7
Factoring by Grouping
Solution
Practice Problem 8
Solution
Practice Problem 9
Factoring Trinomials of the Form Ax2+Bx+C
Solution
Practice Problem 10
Section P.4 Exercises
Concepts and Vocabulary
Building Skills
Applying the Concepts
Beyond the Basics
Getting Ready for the Next Section
Section P.5 Rational Expressions
Before Starting This Section, Review
Objectives
Rational Expressions
Solution
Practice Problem 1
Lowest Terms for a Rational Expression
Solution
Practice Problem 2
Multiplication and Division of Rational Expressions
Solution
Practice Problem 3
Addition and Subtraction of Rational Expressions
Solution
Practice Problem 4
Solution
Practice Problem 5
Solution
Practice Problem 6
Solution
Practice Problem 7
Complex Fractions
Solution
Practice Problem 8
Solution
Practice Problem 9
Section P.5 Exercises
Concepts and Vocabulary
Building Skills
Applying the Concepts
Beyond the Basics
Getting Ready for the Next Section
Section P.6 Rational Exponents and Radicals
Before Starting This Section, Review
Objectives
Square Roots
Solution
Practice Problem 1
Simplifying Square Roots
Solution
Practice Problem 2
Solution
Practice Problem 3
Other Roots
Solution
Practice Problem 4
Solution
Practice Problem 5
Like Radicals
Solution
Practice Problem 6
Radicals with Different Indexes
Solution
Practice Problem 7
Rationalizing Radical Expressions
Solution
Practice Problem 8
Conjugates
Solution
Practice Problem 9
Rational Exponents
Solution
Practice Problem 10
Solution
Practice Problem 11
Solution
Practice Problem 12
Solution
Practice Problem 13
Solution
Practice Problem 14
Section P.6 Exercises
Concepts and Vocabulary
Building Skills
Applying the Concepts
Beyond the Basics
Getting Ready for the Next Section
Chapter P Review and Tests
Review
Review Exercises
Building Skills
Applying the Concepts
Practice Test
Chapter 1 Equations and Inequalities
Topics
Section 1.1 Linear Equations in One Variable
Before Starting this Section, Review
Objectives
Definitions
Solution
Practice Problem 1
Identities, Conditional Equations, and Inconsistent Equations
Equivalent Equations
Solving Linear Equations in One Variable
Practice Problem 2
Solution
Practice Problem 3
Solution
Practice Problem 4
Solution
Practice Problem 5
Solution
Practice Problem 6
Formulas
Solution
Practice Problem 7
Solution
Practice Problem 8
Solution
Practice Problem 9
Section 1.1 Exercises
Concepts and Vocabulary
Building Skills
Applying the Concepts
Beyond the Basics
Critical Thinking/Discussion/Writing
Getting Ready for the Next Section
Section 1.2 Applications of Linear Equations: Modeling
Before Starting this Section, Review
Objectives
Solving Applied Problems
Solution
Practice Problem 1
Geometry
Solution
Practice Problem 2
Finance
Solution
Practice Problem 3
Solution
Practice Problem 4
Uniform Motion
Solution
Practice Problem 5
Solution
Practice Problem 6
Work Rate
Solution
Practice Problem 7
Mixtures
Solution
Practice Problem 8
Section 1.2 Exercises
Concepts and Vocabulary
Building Skills
Applying the Concepts
Beyond the Basics
Critical Thinking/Discussion/Writing
Getting Ready for the Next Section
Section 1.3 Quadratic Equations
Before Starting this Section, Review
Objectives
Factoring Method
Solution
Practice Problem 1
Solution
Practice Problem 2
Solution
Practice Problem 3
The Square Root Method
Solution
Practice Problem 4
Completing the Square
Solution
Practice Problem 5
Solution
Practice Problem 6
The Quadratic Formula
Solution
Practice Problem 7
The Discriminant
Solution
Practice Problem 8
Applications
Solution
Practice Problem 9
Solution
Practice Problem 10
Golden Rectangle
Solution
Practice Problem 11
Section 1.3 Exercises
Concepts and Vocabulary
Building Skills
Applying the Concepts
Beyond the Basics
Critical Thinking/Discussion/Writing
Getting Ready for the Next Section
Section 1.4 Complex Numbers: Quadratic Equations with Complex Solutions
Before Starting this Section, Review
Objectives
Complex Numbers
Solution
Practice Problem 1
Addition and Subtraction
Solution
Practice Problem 2
Multiplying Complex Numbers
Solution
Practice Problem 3
Solution
Practice Problem 4
Complex Conjugates and Division
Solution
Practice Problem 5
Solution
Practice Problem 6
Solution
Practice Problem 7
Quadratic Equations with Complex Solutions
Solution
Practice Problem 8
The Discriminant
Solution
Practice Problem 9
Section 1.4 Exercises
Concepts and Vocabulary
Building Skills
Applying the Concepts
Beyond the Basics
Critical Thinking/Writing/Discussion
Getting Ready for the Next Section
Section 1.5 Solving Other Types of Equations
Before Starting this Section, Review
Objectives
Solving Equations by Factoring
Practice Problem 1
Solution
Practice Problem 2
Rational Equations
Solution
Practice Problem 3
Solution
Practice Problem 4
Equations Involving Radicals
Solution
Practice Problem 5
Solution
Practice Problem 6
Solution
Practice Problem 7
Equations with Rational Exponents
Solution
Practice Problem 8
Equations That Are Quadratic in Form
Solution
Practice Problem 9
Solution
Practice Problem 10
Solution
Practice Problem 11
Section 1.5 Exercises
Concepts and Vocabulary
Building Skills
Applying the Concepts
Beyond the Basics
Critical Thinking/Discussion/Writing
Getting Ready for the Next Section
Section 1.6 Inequalities
Before Starting this Section, Review
Objectives
Inequalities
Linear Inequalities
Solution
Practice Problem 1
Solution
Practice Problem 2
Solution
Practice Problem 3
Combining Two Inequalities
Solution
Practice Problem 4
Solution
Practice Problem 5
Solution
Practice Problem 6
Solution
Practice Problem 7
Solution
Practice Problem 8
Using Test Points to Solve Inequalities
Practice Problem 9
Practice Problem 10
Section 1.6 Exercises
Concepts and Vocabulary
Building Skills
Applying the Concepts
Beyond the Basics
Critical Thinking/Discussion/Writing
Getting Ready for the Next Section
Section 1.7 Equations and Inequalities Involving Absolute Value
Before Starting this Section, Review
Objectives
Equations Involving Absolute Value
Solution
Practice Problem 1
Solution
Practice Problem 2
Solution
Practice Problem 3
Inequalities Involving Absolute Value
Solution
Practice Problem 4
Solution
Practice Problem 5
Solution
Practice Problem 6
Solution
Practice Problem 7
Solution
Practice Problem 8
Section 1.7 Exercises
Concepts and Vocabulary
Building Skills
Applying the Concepts
Beyond the Basics
Critical Thinking/Discussion/Writing
Getting Ready for the Next Section
Chapter 1 Review and Tests
Review
Review Exercises
Building Skills
Applying the Concepts
Practice Test A
Practice Test B
Chapter 2 Graphs and Functions
Topics
Section 2.1 The Coordinate Plane
Before Starting this Section, Review
Objectives
The Coordinate Plane
Solution
Practice Problem 1
Solution
Practice Problem 2
Scales on a Graphing Utility
Distance Formula
Solution
Practice Problem 3
Solution
Practice Problem 4
Solution
Practice Problem 5
Midpoint Formula
Solution
Practice Problem 6
Section 2.1 Exercises
Concepts and Vocabulary
Building Skills
Applying the Concepts
Beyond the Basics
Critical Thinking / Discussion / Writing
Getting Ready for the Next Section
Section 2.2 Graphs of Equations
Before Starting this Section, Review
Objectives
Graph of an Equation
Solution
Practice Problem 1
Comment
Intercepts
Solution
Practice Problem 2
Symmetry
Solution
Practice Problem 3
Practice Problem 4
Solution
Practice Problem 5
Circles
Standard Form
Solution
Practice Problem 6
Solution
Practice Problem 7
Semicircles
General Form
Solution
Practice Problem 8
Section 2.2 Exercises
Concepts and Vocabulary
Building Skills
Applying the Concepts
Beyond the Basics
Critical Thinking / Discussion / Writing
Getting Ready for the Next Section
Section 2.3 Lines
Before Starting this Section, Review
Objectives
Slope of a Line
Solution
Interpretation
Practice Problem 1
Point–Slope Form
Solution
Practice Problem 2
Solution
Practice Problem 3
Slope–Intercept Form
Solution
Practice Problem 4
Solution
Practice Problem 5
Equations of Horizontal and Vertical Lines
Solution
Practice Problem 6
General Form of the Equation of a Line
Solution
Practice Problem 7
Solution
Practice Problem 8
Parallel and Perpendicular Lines
Practice Problem 9
Modeling Data Using Linear Regression
Solution
Practice Problem 10
Section 2.3 Exercises
Concepts and Vocabulary
Building Skills
Applying the Concepts
Beyond the Basics
Critical Thinking / Discussion / Writing
Getting Ready for the Next Section
Section 2.4 Functions
Before Starting this Section, Review
Objectives
Functions
Function Notation
Representations of Functions
Functions Defined by Ordered Pairs
Solution
Practice Problem 1
Functions Defined by Tables and Graphs
Functions Defined by Equations
Solution
Practice Problem 2
Solution
Practice Problem 3
Solution
Practice Problem 4
The Domain of a Function
Solution
Practice Problem 5
The Range of a Function
Solution
Practice Problem 6
Graphs of Functions
Solution
Practice Problem 7
Function Information from Its Graph
Solution
Practice Problem 8
Solution
Practice Problem 9
Building Functions
Level of Drugs in Bloodstream
Solution
Practice Problem 10
Solution
Practice Problem 11
Functions in Economics
Linear Cost Function
Linear Price–Demand Function
Revenue Function R(x)
Profit Function P(x)
Solution
Practice Problem 12
Section 2.4 Exercises
Concepts and Vocabulary
Building Skills
Applying the Concepts
Beyond the Basics
Critical Thinking / Discussion / Writing
Getting Ready for the Next Section
Section 2.5 Properties of Functions
Before Starting this Section, Review
Objectives
Increasing and Decreasing Functions
Solution
Practice Problem 1
Relative Maximum and Minimum Values
Solution
Practice Problem 2
Solution
Practice Problem 3
Solution
Practice Problem 4
Even–Odd Functions and Symmetry
Solution
Practice Problem 5
Solution
Practice Problem 6
Solution
Practice Problem 7
Average Rate of Change
Practice Problem 8
Solution
Practice Problem 9
Solution
Practice Problem 10
Solution
Practice Problem 11
Section 2.5 Exercises
Concepts and Vocabulary
Building Skills
Applying the Concepts
Beyond the Basics
Critical Thinking / Discussion / Writing
Getting Ready for the Next Section
Section 2.6 A Library of Functions
Before Starting this Section, Review
Objectives
Linear Functions
Solution
Practice Problem 1
Solution
Practice Problem 2
Square Root and Cube Root Functions
Square Root Function
Solution
Practice Problem 3
Cube Root Function
Solution
Practice Problem 4
Piecewise Functions
Practice Problem 5
Solution
Practice Problem 6
Solution
Practice Problem 7
Graphing Piecewise Functions
Solution
Practice Problem 8
Solution
Practice Problem 9
Basic Functions
Section 2.6 Exercises
Concepts and Vocabulary
Building Skills
Applying the Concepts
Beyond the Basics
Critical Thinking / Discussion / Writing
Getting Ready for the Next Section
Section 2.7 Transformations of Functions
Before Starting this Section, Review
Objectives
Transformations
Vertical and Horizontal Shifts
Solution
Practice Problem 1
Solution
Practice Problem 2
Practice Problem 3
Reflections
Comparing the Graphs of y=f(x) and y=−f(x)
Comparing the Graphs of y=f(x) and y=f(−x)
Solution
Practice Problem 4
Solution
Practice Problem 5
Stretching or Compressing
Comparing the Graphs of y=f(x) and y=af(x)
Solution
Practice Problem 6
Comparing the Graphs of y=f(x) and y=f(bx)
Solution
Practice Problem 7
Multiple Transformations in Sequence
Solution
Practice Problem 8
Solution
Practice Problem 9
Section 2.7 Exercises
Concepts and Vocabulary
Building Skills
Applying the Concepts
Beyond the Basics
Critical Thinking / Discussion / Writing
Getting Ready for the Next Section
Section 2.8 Combining Functions; Composite Functions
Before Starting this Section, Review
Objectives
Combining Functions
Solution
Practice Problem 1
Solution
Practice Problem 2
Composition of Functions
Evaluating (f∘g)(x)
Solution
Practice Problem 3
Solution
Practice Problem 4
Domain of Composite Functions
Practice Problem 5
Solution
Practice Problem 6
Solution
Practice Problem 7
Decomposition of a Function
Practice Problem 8
Applications of Composite Functions
Solution
Practice Problem 9
Solution
Practice Problem 10
Section 2.8 Exercises
Concepts and Vocabulary
Building Skills
Applying the Concepts
Beyond the Basics
Critical Thinking / Discussion / Writing
Getting Ready for the Next Section
Section 2.9 Inverse Functions
Before Starting this Section, Review
Objectives
Inverses
Solution
Practice Problem 1
Solution
Practice Problem 2
Solution
Practice Problem 3
Finding the Inverse Function
Solution
Practice Problem 4
Practice Problem 5
Solution
Practice Problem 6
Finding the Range of a One-to-One Function
Solution
Practice Problem 7
Solution
Practice Problem 8
Applications
Solution
Practice Problem 9
Section 2.9 Exercises
Concepts and Vocabulary
Building Skills
Applying the Concepts
Beyond the Basics
Critical Thinking / Discussion / Writing
Getting Ready for the Next Section
Chapter 2 Review and Tests
Review
Review Exercises
Building Skills
Applying the Concepts
Practice Test A
Practice Test B
Cumulative Review Exercises Chapters P–2
Chapter 3 Polynomial and Rational Functions
Topics
Section 3.1 Quadratic Functions
Before Starting this Section, Review
Objectives
Quadratic Functions
Standard Form of a Quadratic Function
Solution
Practice Problem 1
Practice Problem 2
Graphing a Quadratic Function f(x)=ax2+bx+c
Converting f(x)=ax2+bx+c to Standard Form
Practice Problem 3
Solution
Practice Problem 4
Applications
Solution
Practice Problem 5
Solution
Practice Problem 6
Section 3.1 Exercises
Concepts and Vocabulary
Building Skills
Applying the Concepts
Beyond the Basics
Critical Thinking / Discussion / Writing
Getting Ready for the Next Section
Section 3.3 Dividing Polynomials
Before Starting this Section, Review
Objectives
The Division Algorithm
Practice Problem 1
Solution
Practice Problem 2
Synthetic Division
Practice Problem 3
Solution
Practice Problem 4
The Remainder and Factor Theorems
Solution
Practice Problem 5
Solution
Practice Problem 6
Solution
Practice Problem 7
Application
Solution
Practice Problem 8
Section 3.3 Exercises
Concepts and Vocabulary
Building Skills
Applying the Concepts
Beyond the Basics
Critical Thinking / Discussion / Writing
Getting Ready for the Next Section
Section 3.4 The Real Zeros of a Polynomial Function
Before Starting this Section, Review
Objectives
Real Zeros of a Polynomial Function
Rational Zeros Theorem
Solution
Practice Problem 1
Solution
Practice Problem 2
Descartes’s Rule of Signs
Solution
Practice Problem 3
Bounds on the Real Zeros
Solution
Practice Problem 4
Find the Real Zeros of a Polynomial Function
Solution
Practice Problem 5
Solution
Practice Problem 6
Section 3.4 Exercises
Concepts and Vocabulary
Building Skills
Applying the Concepts
Beyond the Basics
Critical Thinking / Discussion / Writing
Getting Ready for the Next Section
Section 3.5 The Complex Zeros of a Polynomial Function
Before Starting this Section, Review
Objectives
Solution
Practice Problem 1
Conjugate Pairs Theorem
Solution
Practice Problem 2
Solution
Practice Problem 3
Solution
Practice Problem 4
Section 3.5 Exercises
Concepts and Vocabulary
Building Skills
Beyond the Basics
Critical Thinking / Discussion / Writing
Getting Ready for the Next Section
Section 3.6 Rational Functions
Before Starting this Section, Review
Objectives
Rational Functions
Solution
Practice Problem 1
Vertical and Horizontal Asymptotes
Translations of f(x)=1x
Solution
Practice Problem 2
Solution
Practice Problem 3
Solution
Practice Problem 4
Solution
Practice Problem 5
Graphing Rational Functions
Practice Problem 6
Solution
Practice Problem 7
Solution
Practice Problem 8
Oblique Asymptotes
Solution
Practice Problem 9
Graph of a Revenue Curve
Solution
Practice Problem 10
Section 3.6 Exercises
Concepts and Vocabulary
Building Skills
Applying the Concepts
Beyond the Basics
Critical Thinking / Discussion / Writing
Getting Ready for the Next Section
Section 3.7 Variation
Before Starting this Section, Review
Objectives
Direct Variation
Practice Problem 1
Solution
Practice Problem 2
Solution
Practice Problem 3
Inverse Variation
Solution
Practice Problem 4
Solution
Practice Problem 5
Joint and Combined Variation
Solution
Practice Problem 6
Section 3.7 Exercises
Concepts and Vocabulary
Building Skills
Applying the Concepts
Beyond the Basics
Critical Thinking / Discussion / Writing
Getting Ready for the Next Section
Chapter 3 Review and Tests
Review
Review Exercises
Building Skills
Applying the Concepts
Practice Test A
Practice Test B
Cumulative Review Exercises Chapters P–3
Chapter 4 Exponential and Logarithmic Functions
Topics
Section 4.1 Exponential Functions
Before Starting this Section, Review
Objectives
Exponential Functions
Evaluate Exponential Functions
Solution
Practice Problem 1
Solution
Practice Problem 2
Graphing Exponential Functions
Solution
Practice Problem 3
Transformations on Exponential Functions
Solution
Practice Problem 4
Solution
Practice Problem 5
Solution
Practice Problem 6
Simple Interest
Solution
Practice Problem 7
Compound Interest
Solution
Practice Problem 8
Solution
Practice Problem 9
Solution
Practice Problem 10
Continuous Compound Interest Formula
Continuous Compounding
Solution
Practice Problem 11
The Natural Exponential Function
Exponential Growth and Decay
Solution
Practice Problem 12
Solution
Practice Problem 13
Section 4.1 Exercises
Concepts and Vocabulary
Building Skills
Applying the Concepts
Beyond the Basics
Critical Thinking / Discussion / Writing
Getting Ready for the Next Section
Section 4.2 Logarithmic Functions
Before Starting this Section, Review
Objectives
Logarithmic Functions
Solution
Practice Problem 1
Solution
Practice Problem 2
Evaluating Logarithms
Solution
Practice Problem 3
Basic Properties of Logarithms
Solution
Practice Problem 4
Domains of Logarithmic Functions
Solution
Practice Problem 5
Graphs of Logarithmic Functions
Practice Problem 6
Solution
Practice Problem 7
Solution
Practice Problem 8
Common Logarithm
Solution
Practice Problem 9
Natural Logarithm
Solution
Practice Problem 10
Investments
Solution
Practice Problem 11
Newton’s Law of Cooling
Solution
Practice Problem 12
Section 4.2 Exercises
Concepts and Vocabulary
Building Skills
Applying the Concepts
Beyond the Basics
Critical Thinking / Discussion / Writing
Getting Ready for the Next Section
Section 4.3 Rules of Logarithms
Before Starting this Section, Review
Objectives
Rules of Logarithms
Solution
Practice Problem 1
Solution
Practice Problem 2
Solution
Practice Problem 3
Number of Digits
Solution
Practice Problem 4
Change of Base
Solution
Practice Problem 5
Solution
Practice Problem 6
Growth and Decay
Half-Life
Solution
Practice Problem 7
Radiocarbon Dating
Solution
Practice Problem 8
Section 4.3 Exercises
Concepts and Vocabulary
Building Skills
Applying the Concepts
Beyond the Basics
Critical Thinking / Discussion / Writing
Getting Ready for the Next Section
Section 4.4 Exponential and Logarithmic Equations and Inequalities
Before Starting this Section, Review
Objectives
Solving Exponential Equations
Solution
Practice Problem 1
Practice Problem 2
Solution
Practice Problem 3
Solution
Practice Problem 4
Applications of Exponential Equations
Solution
Practice Problem 5
Solving Logarithmic Equations
Practice Problem 6
Solution
Practice Problem 7
Solution
Practice Problem 8
Solution
Practice Problem 9
Logarithmic and Exponential Inequalities
Solution
Practice Problem 10
Solution
Practice Problem 11
Section 4.4 Exercises
Concepts and Vocabulary
Building Skills
Applying the Concepts
Beyond the Basics
Critical Thinking / Discussion / Writing
Getting Ready for the Next Section
Section 4.5 Logarithmic Scales; Modeling
Before Starting this Section, Review
Objectives
pH Scale
Solution
Practice Problem 1
Solution
Practice Problem 2
Earthquake Intensity
Solution
Practice Problem 3
Solution
Practice Problem 4
Energy of an Earthquake
Solution
Practice Problem 5
Loudness of Sound
Solution
Practice Problem 6
Solution
Practice Problem 7
Solution
Practice Problem 8
Musical Pitch
Solution
Practice Problem 9
Solution
Practice Problem 10
Star Brightness
Solution
Practice Problem 11
Modeling
Solution
Practice Problem 12
Solution
Practice Problem 13
Section 4.5 Exercises
Concepts and Vocabulary
Building Skills
Applying the Concepts
Beyond the Basics
Getting Ready for the Next Section
Chapter 4 Review and Tests
Review
Review Exercises
Concepts and Vocabulary
Building Skills
Applying the Concepts
Practice Test A
Practice Test B
Cumulative Review Exercises Chapters P–4
Chapter 5 Systems of Equations and Inequalities
Topics
Section 5.1 Systems of Linear Equations in Two Variables
Before Starting this Section, Review
Objectives
System of Equations
Solution
Practice Problem 1
Graphical Method
Solution
Practice Problem 2
Substitution Method
Practice Problem 3
Solution
Practice Problem 4
Solution
Practice Problem 5
Elimination Method
Practice Problem 6
Solution
Practice Problem 7
Applications
Solution
Practice Problem 8
Solution
Practice Problem 9
Section 5.1 Exercises
Concepts and Vocabulary
Building Skills
Applying the Concepts
Beyond the Basics
Critical Thinking / Discussion / Writing
Getting Ready for the Next Section
Section 5.2 Systems of Linear Equations in Three Variables
Before Starting this Section, Review
Objectives
Systems of Linear Equations
Solution
Practice Problem 1
Practice Problem 2
Number of Solutions of a Linear System
Solution
Practice Problem 3
Solution
Practice Problem 4
Nonsquare Systems
Solution
Practice Problem 5
Geometric Interpretation
An Application to CAT Scans
Solution
Practice Problem 6
Section 5.2 Exercises
Concepts and Vocabulary
Building Skills
Applying the Concepts
Beyond the Basics
Critical Thinking / Discussion / Writing
Getting Ready for the Next Section
Section 5.3 Partial-Fraction Decomposition
Before Starting this Section, Review
Objectives
Partial Fractions
Q(x) Has Only Distinct Linear Factors
Practice Problem 1
Solution
Practice Problem 2
Q(x) Has Repeated Linear Factors
Solution
Practice Problem 3
Solution
Practice Problem 4
Q(x) Has Distinct Irreducible Quadratic Factors
Solution
Practice Problem 5
Q(x) Has Repeated Irreducible Quadratic Factors
Solution
Practice Problem 6
Solution
Practice Problem 7
Solution
Practice Problem 8
Section 5.3 Exercises
Concepts and Vocabulary
Building Skills
Applying the Concepts
Beyond the Basics
Critical Thinking / Discussion / Writing
Getting Ready for the Next Section
Section 5.4 Systems of Nonlinear Equations
Before Starting this Section, Review
Objectives
Systems of Nonlinear Equations
Solving Systems of Nonlinear Equations by Substitution
Solution
Practice Problem 1
Solving Systems of Nonlinear Equations by Elimination
Solution
Practice Problem 2
Applications
Solution
Practice Problem 3
Section 5.4 Exercises
Concepts and Vocabulary
Building Skills
Applying the Concepts
Beyond the Basics
Critical Thinking / Discussion / Writing
Getting Ready for the Next Section
Section 5.5 Systems of Inequalities
Before Starting this Section, Review
Objectives
Graph of a Linear Inequality in Two Variables
Solution
Practice Problem 1
Practice Problem 2
Solution
Practice Problem 3
Systems of Linear Inequalities in Two Variables
Solution
Practice Problem 4
Solution
Practice Problem 5
Nonlinear Inequality
Practice Problem 6
Nonlinear Systems
Solution
Practice Problem 7
Section 5.5 Exercises
Concepts and Vocabulary
Building Skills
Applying the Concepts
Beyond the Basics
Critical Thinking / Discussion / Writing
Getting Ready for the Next Section
Section 5.6 Linear Programming
Before Starting this Section, Review
Objectives
Linear Programming
Solving Linear Programming Problems
Practice Problem 1
Solution
Practice Problem 2
Applications
Solution
Practice Problem 3
Section 5.6 Exercises
Concepts and Vocabulary
Building Skills
Applying the Concepts
Beyond the Basics
Critical Thinking / Discussion / Writing
Getting Ready for the Next Section
Chapter 5 Review and Tests
Review
Review Exercises
Building Skills
Applying the Concepts
Practice Test A
Practice Test B
Cumulative Review Exercises Chapters P–5
Chapter 6 Matrices and Determinants
Topics
Section 6.1 Matrices and Systems of Equations
Before Starting this Section, Review
Objectives
Definition of a Matrix
Solution
Practice Problem 1
Using Matrices to Solve Linear Systems
Solution
Practice Problem 2
Solution
Practice Problem 3
Solution
Practice Problem 4
Gaussian Elimination
Practice Problem 5
Solution
Practice Problem 6
Solution
Practice Problem 7
Gauss–Jordan Elimination
Solution
Practice Problem 8
Solution
Practice Problem 9
Solution
Practice Problem 10
Section 6.1 Exercises
Concepts and Vocabulary
Building Skills
Applying the Concepts
Beyond the Basics
Critical Thinking/Discussion/Writing
Getting Ready for the Next Section
Section 6.2 Matrix Algebra
Before Starting this Section, Review
Objectives
Equality of Matrices
Solution
Practice Problem 1
Matrix Addition and Scalar Multiplication
Solution
Practice Problem 2
Solution
Practice Problem 3
Solution
Practice Problem 4
Matrix Multiplication
Solution
Practice Problem 5
Solution
Practice Problem 6
Solution
Practice Problem 7
Solution
Practice Problem 8
Solution
Practice Problem 9
Computer Graphics
Solution
Practice Problem 10
Section 6.2 Exercises
Concepts and Vocabulary
Building Skills
Applying the Concepts
Beyond the Basics
Critical Thinking/Discussion/Writing
Getting Ready for the Next Section
Section 6.3 The Matrix Inverse
Before Starting this Section, Review
Objectives
The Multiplicative Inverse of a Matrix
Solution
Practice Problem 1
Solution
Practice Problem 2
Finding the Inverse of a Matrix
Solution
Practice Problem 3
Solution
Practice Problem 4
A Rule for Finding the Inverse of a 2×2 Matrix
Solution
Practice Problem 5
Solving Systems of Linear Equations by Using Matrix Inverses
Solution
Practice Problem 6
Applications of Matrix Inverses
The Leontief Input–Output Model
Solution
Practice Problem 7
Cryptography
Solution
Practice Problem 8
Section 6.3 Exercises
Concepts and Vocabulary
Building Skills
Applying the Concepts
Beyond the Basics
Critical Thinking/Discussion/Writing
Getting Ready for the Next Section
Section 6.4 Determinants and Cramer’s Rule Determinants and Cramer’s Rule
Before Starting this Section, Review
Objectives
The Determinant of a 2×2 Matrix
Solution
Practice Problem 1
Minors and Cofactors
Solution
Practice Problem 2
The Determinant of an n×n Matrix
Solution
Practice Problem 3
Cramer’s Rule
Solution
Practice Problem 4
Solution
Practice Problem 5
Applications
Solution
Practice Problem 6
Section 6.4 Exercises
Concepts and Vocabulary
Building Skills
Applying the Concepts
Beyond the Basics
Critical Thinking/Discussion/Writing
Getting Ready for the Next Section
Chapter 6 Review and Tests
Review
Review Exercises
Concepts and Vocabulary
Applying the Concepts
Practice Test A
Practice Test B
Cumulative Review Exercises Chapters P–6
Chapter 7 Conic Sections
Topics
Section 7.1 Conic Sections: Overview
Section 7.2 The Parabola
Before Starting this Section, Review
Objectives
Geometric Definition of a Parabola
Equation of a Parabola
Solution
Practice Problem 1
Solution
Practice Problem 2
Solution
Practice Problem 3
Translations of Parabolas
Solution
Practice Problem 4
Solution
Practice Problem 5
Solution
Practice Problem 6
Reflecting Property of Parabolas
Solution
Practice Problem 7
Section 7.2 Exercises
Concepts and Vocabulary
Building Skills
Applying the Concepts
Beyond the Basics
Critical Thinking/Discussion/Writing
Getting Ready for the Next Section
Section 7.3 The Ellipse
Before Starting this Section, Review
Objectives
Definition of Ellipse
Equation of an Ellipse
Solution
Practice Problem 1
Solution
Practice Problem 2
Translations of Ellipses
Solution
Practice Problem 3
Solution
Practice Problem 4
Solution
Practice Problem 5
Applications
Solution
Practice Problem 6
Section 7.3 Exercises
Concepts and Vocabulary
Building Skills
Applying the Concepts
Beyond the Basics
Critical Thinking/Discussion/Writing
Getting Ready for the Next Section
Section 7.4 The Hyperbola
Before Starting this Section, Review
Objectives
Definition of Hyperbola
Solution
Practice Problem 1
Solution
Practice Problem 2
Solution
Practice Problem 3
The Asymptotes of a Hyperbola
Solution
Practice Problem 4
Solution
Practice Problem 5
Graphing a Hyperbola with Center (0, 0)
Practice Problem 6
Translations of Hyperbolas
Solution
Practice Problem 7
Solution
Practice Problem 8
Applications
Solution
Practice Problem 9
Section 7.4 Exercises
Concepts and Vocabulary
Building Skills
Applying the Concepts
Beyond the Basics
Critical Thinking/Discussion/Writing
Getting Ready for the Next Section
Chapter 7 Review and Tests
Review
Review Exercises
Practice Test A
Practice Test B
Cumulative Review Exercises Chapters P–7
Chapter 8 Further Topics in Algebra
Topics
Section 8.1 Sequences and Series
Before Starting this Section, Review
Objectives
Sequences
Solution
Practice Problem 1
Solution
Practice Problem 2
Solution
Practice Problem 3
Recursive Formulas
Solution
Practice Problem 4
Solution
Practice Problem 5
Factorial Notation
Solution
Practice Problem 6
Solution
Practice Problem 7
Summation Notation
Solution
Practice Problem 8
Series
Solution
Practice Problem 9
Section 8.1 Exercises
Concepts and Vocabulary
Building Skills
Applying the Concepts
Beyond the Basics
Critical Thinking / Discussion / Writing
Getting Ready for the Next Section
Section 8.2 Arithmetic Sequences; Partial Sums
Before Starting this Section, Review
Objectives
Arithmetic Sequence
Solution
Practice Problem 1
Solution
Practice Problem 2
Solution
Practice Problem 3
Solution
Practice Problem 4
Sum of a Finite Arithmetic Sequence
Solution
Practice Problem 5
Solution
Practice Problem 6
Section 8.2 Exercises
Concepts and Vocabulary
Building Skills
Applying the Concepts
Beyond the Basics
Critical Thinking / Discussion / Writing
Getting Ready for the Next Section
Section 8.3 Geometric Sequences and Series
Before Starting this Section, Review
Objectives
Geometric Sequence
Solution
Practice Problem 1
Solution
Practice Problem 2
Solution
Practice Problem 3
Solution
Practice Problem 4
Solution
Practice Problem 5
Solution
Practice Problem 6
Finding the Sum of a Finite Geometric Sequence
Solution
Practice Problem 7
Annuities
Solution
Practice Problem 8
Infinite Geometric Series
Solution
Practice Problem 9
Solution
Practice Problem 10
Section 8.3 Exercises
Concepts and Vocabulary
Building Skills
Applying the Concepts
Beyond the Basics
Critical Thinking / Discussion / Writing
Getting Ready for the Next Section
Section 8.4 Mathematical Induction
Before Starting this Section, Review
Objective
Mathematical Induction
Determining the Statement Pk+1 from the Statement Pk
Solution
Practice Problem 1
Solution
Practice Problem 2
Solution
Practice Problem 3
Section 8.4 Exercises
Concepts and Vocabulary
Building Skills
Applying the Concepts
Beyond the Basics
Critical Thinking / Discussion / Writing
Getting Ready for the Next Section
Section 8.5 The Binomial Theorem
Before Starting this Section, Review
Objectives
Pascal’s Triangle
Solution
Practice Problem 1
The Binomial Theorem
Solution
Practice Problem 2
Solution
Practice Problem 3
Binomial Coefficients
Solution
Practice Problem 4
Solution
Practice Problem 5
Solution
Practice Problem 6
Section 8.5 Exercises
Concepts and Vocabulary
Building Skills
Beyond the Basics
Critical Thinking / Discussion / Writing
Getting Ready for the Next Section
Section 8.6 Counting Principles
Before Starting this Section, Review
Objectives
Fundamental Counting Principle
Solution
Practice Problem 1
Solution
Practice Problem 2
Solution
Practice Problem 3
Permutations
Solution
Practice Problem 4
Solution
Practice Problem 5
Solution
Practice Problem 6
Combinations
Solution
Practice Problem 7
Solution
Practice Problem 8
Solution
Practice Problem 9
Distinguishable Permutations
Solution
Practice Problem 10
Deciding Whether to Use Permutations, Combinations, or the Fundamental Counting Principle
Section 8.6 Exercises
Concepts and Vocabulary
Building Skills
Applying the Concepts
Beyond the Basics
Critical Thinking / Discussion / Writing
Getting Ready for the Next Section
Section 8.7 Probability
Before Starting this Section, Review
Objectives
The Probability of an Event
Solution
Practice Problem 1
Solution
Practice Problem 2
Solution
Practice Problem 3
Solution
Practice Problem 4
The Additive Rule
Mutually Exclusive Events
Solution
Practice Problem 5
The Complement of an Event
Solution
Practice Problem 6
Experimental Probabilities
Solution
Practice Problem 7
Section 8.7 Exercises
Concepts and Vocabulary
Building Skills
Applying the Concepts
Beyond the Basics
Critical Thinking / Discussion / Writing
Chapter 8 Review and Tests
Review
Review Exercises
Practice Test A
Practice Test B
Cumulative Review Exercises Chapters P–8
Answers
Chapter P
Section P.1
Concepts and Vocabulary
Building Skills
Applying the Concepts
Beyond the Basics
Getting Ready for the Next Section
Section P.2
Concepts and Vocabulary
Building Skills
Applying the Concepts
Beyond the Basics
Getting Ready for the Next Section
Section P.3
Concepts and Vocabulary
Building Skills
Applying the Concepts
Beyond the Basics
Getting Ready for the Next Section
Section P.4
Concepts and Vocabulary
Building Skills
Applying the Concepts
Beyond the Basics
Getting Ready for the Next Section
Section P.5
Concepts and Vocabulary
Building Skills
Applying the Concepts
Beyond the Basics
Getting Ready for the Next Section
Section P.6
Concepts and Vocabulary
Building Skills
Applying the Concepts
Beyond the Basics
Getting Ready for the Next Section
Review Exercises
Applying the Concepts
Practice Test
Chapter 1
Section 1.1
Concepts and Vocabulary
Building Skills
Applying the Concepts
Beyond the Basics
Critical Thinking/Discussion/Writing
Getting Ready for the Next Section
Section 1.2
Concepts and Vocabulary
Building Skills
Applying the Concepts
Beyond the Basics
Critical Thinking/Discussion/Writing
Getting Ready for the Next Section
Section 1.3
Concepts and Vocabulary
Building Skills
Applying the Concepts
Beyond the Basics
Getting Ready for the Next Section
Section 1.4
Concepts and Vocabulary
Building Skills
Applying the Concepts
Beyond the Basics
Critical Thinking/Discussion/Writing
Getting Ready for the Next Section
Section 1.5
Concepts and Vocabulary
Building Skills
Applying the Concepts
Beyond the Basics
Critical Thinking/Discussion/Writing
Getting Ready for the Next Section
Section 1.6
Concepts and Vocabulary
Building Skills
Applying the Concepts
Beyond the Basics
Critical Thinking/Discussion/Writing
Getting Ready for the Next Section
Section 1.7
Concepts and Vocabulary
Building Skills
Applying the Concepts
Beyond the Basics
Critical Thinking/Discussion/Writing
Getting Ready for the Next Section
Review Exercises
Building Skills
Applying the Concepts
Practice Test A
Practice Test B
Chapter 2
Section 2.1
Concepts and Vocabulary
Building Skills
Applying the Concepts
Beyond the Basics
Critical Thinking / Discussion / Writing
Getting Ready for the Next Section
Section 2.2
Concepts and Vocabulary
Building Skills
Applying the Concepts
Beyond the Basics
Critical Thinking / Discussion / Writing
Getting Ready for the Next Section
Section 2.3
Building Skills
Applying the Concepts
Beyond the Basics
Critical Thinking / Discussion / Writing
Getting Ready for the Next Section
Section 2.4
Concepts and Vocabulary
Building Skills
Applying the Concepts
Beyond the Basics
Critical Thinking / Discussion / Writing
Section 2.5
Concepts and Vocabulary
Building Skills
Applying the Concepts
Beyond the Basics
Critical Thinking / Discussion / Writing
Getting Ready for the Next Section
Section 2.6
Concepts and Vocabulary
Building Skills
Applying the Concepts
Beyond the Basics
Critical Thinking / Discussion / Writing
Getting Ready for the Next Section
Section 2.7
Concepts and Vocabulary
Building Skills
Applying the Concepts
Beyond the Basics
Critical Thinking / Discussion / Writing
Getting Ready for the Next Section
Section 2.8
Concepts and Vocabulary
Building Skills
Applying the Concepts
Beyond the Basics
Critical Thinking / Discussion / Writing
Getting Ready for the Next Section
Section 2.9
Concepts and Vocabulary
Building Skills
Applying the Concepts
Beyond the Basics
Critical Thinking / Discussion / Writing
Getting Ready for the Next Section
Review Exercises
Applying the Concepts
Practice Test A
Practice Test B
Cumulative Review Exercises (Chapters P–2)
Chapter 3
Section 3.1
Concepts and Vocabulary
Building Skills
Applying the Concepts
Beyond the Basics
Getting Ready for the Next Section
Section 3.2
Concepts and Vocabulary
Building Skills
Applying the Concepts
Beyond the Basics
Critical Thinking / Discussion / Writing
Getting Ready for the Next Section
Section 3.3
Concepts and Vocabulary
Building Skills
Applying the Concepts
Beyond the Basics
Getting Ready for the Next Section
Section 3.4
Concepts and Vocabulary
Building Skills
Applying the Concepts
Beyond the Basics
Getting Ready for the Next Section
Section 3.5
Concepts and Vocabulary
Building Skills
Beyond the Basics
Critical Thinking / Discussion / Writers
Getting Ready for the Next Section
Section 3.6
Concepts and Vocabulary
Building Skills
Applying the Concepts
Beyond the Basics
Critical Thinking / Discussion / Writing
Getting Ready for the Next Section
Section 3.7
Concepts and Vocabulary
Building Skills
Applying the Concepts
Beyond the Basics
Critical Thinking / Discussion / Writing
Getting Ready for the Next Section
Review Exercises
Building Skills
Applying the Concepts
Practice Test A
Practice Test B
Cumulative Review Exercises (Chapters P–3)
Chapter 4
Section 4.1
Concepts and Vocabulary
Building Skills
Applying the Concept
Beyond the Basics
Getting Ready for the Next Section
Section 4.2
Concepts and Vocabulary
Building Skills
Applying the Concepts
Beyond the Basics
Critical Thinking / Discussion / Writing
Getting Ready for the Next Section
Section 4.3
Concepts and Vocabulary
Building Skills
Applying the Concepts
Beyond the Basics
Critical Thinking / Discussion / Writing
Getting Ready for the Next Section
Section 4.4
Concepts and Vocabulary
Building Skills
Applying the Concepts
Beyond the Basics
Critical Thinking / Discussion / Writing
Getting Ready for the Next Section
Section 4.5
Concepts and Vocabulary
Building Skills
Applying the Concepts
Beyond the Basics
Getting Ready for the Next Section
Review Exercises
Concepts and Vocabulary
Building Skills
Applying the Concepts
Practice Test A
Practice Test B
Cumulative Review Exercises (Chapters P–4)
Chapter 5
Section 5.1
Concepts and Vocabulary
Building Skills
Applying the Concepts
Getting Ready for the Next Section
Section 5.2
Concepts and Vocabulary
Building Skills
Applying the Concepts
Beyond the Basics
Critical Thinking / Discussion / Writing
Getting Ready for the Next Section
Section 5.3
Concepts and Vocabulary
Building Skills
Applying the Concepts
Beyond the Basics
Getting Ready for the Next Section
Section 5.4
Basic Concepts and Skills
Applying the Concepts
Beyond the Basics
Critical Thinking / Discussion / Writing
Getting Ready for the Next Section
Section 5.5
Concepts and Vocabulary
Building Skills
Applying the Concepts
Beyond the Basics
Critical Thinking / Discussion / Writing
Getting Ready for the Next Section
Section 5.6
Basic Concepts and Skills
Applying the Concepts
Beyond the Basics
Critical Thinking / Discussion / Writing
Getting Ready for the Next Section
Review Exercises
Building Skills
Applying the Concepts
Practice Test A
Practice Test B
Cumulative Review Exercises (Chapters P–8)
Chapter 6
Section 6.1
Concepts and Vocabulary
Building Skills
Applying the Concepts
Beyond the Basics
Getting Ready for the Next Section
Section 6.2
Concepts and Vocabulary
Building Skills
Applying the Concepts
Beyond the Basics
Critical Thinking / Discussion / Writing
Getting Ready for the Next Section
Section 6.3
Building Skills
Applying the Concepts
Beyond the Basics
Critical Thinking / Discussion / Writing
Getting Ready for the Next Section
Section 6.4
Concepts and Vocabulary
Building Skills
Applying the Concepts
Beyond the Basics
Critical Thinking / Discussion / Writing
Getting Ready for the Next Section
Review Exercises
Practice Test A
Practice Test B
Cumulative Review Exercises (Chapters P–9)
Chapter 7
Section 7.2
Concepts and Vocabulary
Building Skills
Applying the Concepts
Beyond the Basics
Critical Thinking / Discussion / Writing
Getting Ready for the Next Section
Section 7.3
Concepts and Vocabulary
Building Skills
Applying the Concepts
Beyond the Basics
Critical Thinking / Discussion / Writing
Getting Ready for the Next Section
Section 7.4
Concepts and Vocabulary
Building Skills
Applying the Concepts
Beyond the Basics
Critical Thinking / Discussion / Writing
Getting Ready for the Next Section
Review Exercises
Practice Test A
Practice Test B
Cumulative Review Exercises (Chapters P–7)
Chapter 8
Section 8.1
Concepts and Vocabulary
Applying the Concepts
Beyond the Basics
Critical Thinking/Discussion/Writing
Getting Ready for the Next Section
Section 8.2
Concepts and Vocabulary
Building Skills
Applying the Concepts
Beyond the Basics
Critical Thinking/Discussion/Writing
Getting Ready for the Next Section
Section 8.3
Concepts and Vocabulary
Building Skills
Applying the Concepts
Beyond the Basics
Critical Thinking/Discussion/Writing
Getting Ready for the Next Section
Section 8.4
Concepts and Vocabulary
Building Skills
Applying the Concepts
Getting Ready for the Next Section
Section 8.5
Concepts and Vocabulary
Building Skills
Beyond the Basics
Getting Ready for the Next Section
Section 8.6
Concepts and Vocabulary
Building Skills
Beyond the Basics
Critical Thinking/Discussion/Writing
Getting Ready for the Next Section
Section 8.7
Concepts and Vocabulary
Building Skills
Applying the Concepts
Beyond the Basics
Critical Thinking/Discussion/Writing
Review Exercises
Practice Test A
Practice Test B
Cumulative Review Exercises (Chapters P–8)
Credits
Index
A
B
C
D
E
F
G
H
I
J
K
L
M
N
O
P
Q
R
S
T
U
V
W
X
Y
Z
Algebra–Formulas and Definitions
Geometry–Formulas
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