College Algebra 7th Edition by Robert Blitzer eBook [PDF]
COLLEGE ALGEBRA
COLLEGE ALGEBRA
CONTENTS
PREFACE
What’s New in the Seventh Edition?
What Content and Organizational Changes Have Been Made to the Seventh Ed
...
College Algebra 7th Edition by Robert Blitzer eBook [PDF]
COLLEGE ALGEBRA
COLLEGE ALGEBRA
CONTENTS
PREFACE
What’s New in the Seventh Edition?
What Content and Organizational Changes Have Been Made to the Seventh Edition?
What Familiar Features Have Been Retained in the Seventh Edition?
Get the Most Out of MyMathLab®
MyMathLab Online Course for College Algebra by Robert Blitzer (access code required)
Resources for Success
TO THE STUDENT
ABOUT THE AUTHOR
APPLICATIONS INDEX
A
B
C
D
E
F
G
H
I
J
K
L
M
N
O
P
R
S
T
U
V
W
X
CHAPTER P Prerequisites: Fundamental Concepts of Algebra
Section P.1 Algebraic Expressions, Mathematical Models, and Real Numbers
What am I Supposed to learn?
Algebraic Expressions
Evaluating Algebraic Expressions
Formulas and Mathematical Models
Sets
The Set of Real Numbers
The Real Number Line
Ordering the Real Numbers
Absolute Value
Properties of Real Numbers and Algebraic Expressions
Simplifying Algebraic Expressions
Properties of Negatives
SOLUTION
Check Point 9
CONCEPT AND VOCABULARY CHECK
EXERCISE SET P.1
Practice Exercises
Practice Plus
Application Exercises
Explaining the Concepts
Critical Thinking Exercises
Preview Exercises
Section P.2 Exponents and Scientific Notation
What am I Supposed to learn?
The Product and Quotient Rules
Zero as an Exponent
Negative Integers as Exponents
The Power Rule for Exponents (Powers to Powers)
The Products-to-Powers Rule for Exponents
The Quotients-to-Powers Rule for Exponents
Simplifying Exponential Expressions
Scientific Notation
Converting from Scientific to Decimal Notation
SOLUTION
Check Point 8
Converting from Decimal to Scientific Notation
SOLUTION
Check Point 9
SOLUTION
Check Point 10
Computations with Scientific Notation
SOLUTION
Check Point 11
Applications: Putting Numbers in Perspective
SOLUTION
Check Point 12
CONCEPT AND VOCABULARY CHECK
EXERCISE SET P.2
Practice Exercises
Practice Plus
Application Exercises
Explaining the Concepts
Critical Thinking Exercises
Group Exercise
Preview Exercises
Section P.3 Radicals and Rational Exponents
What am I Supposed to learn?
Square Roots
Simplifying Expressions of the Form a2
The Product Rule for Square Roots
The Quotient Rule for Square Roots
Adding and Subtracting Square Roots
Rationalizing Denominators
Other kinds of Roots
The Product and Quotient Rules for Other Roots
SOLUTION
Check Point 8
SOLUTION
Check Point 9
Rational Exponents
CONCEPT AND VOCABULARY CHECK
EXERCISE SET P.3
Practice Exercises
Practice Plus
Application Exercises
Writing in Mathematics
Critical Thinking Exercises
Preview Exercises
Section P.4 Polynomials
What am I Supposed to learn?
How We Define Polynomials
How We Describe Polynomials
Adding and Subtracting Polynomials
Multiplying Polynomials
The Product of Two Binomials: FOIL
Multiplying the Sum and Difference of Two Terms
The Square of a Binomial
SOLUTION
Check Point 5
SOLUTION
Check Point 6
Special Products
Polynomials in Several Variables
CONCEPT AND VOCABULARY CHECK
EXERCISE SET P.4
Practice Exercises
Practice Plus
Application Exercises
Explaining the Concepts
Critical Thinking Exercises
Preview Exercises
CHAPTER P Mid-Chapter Check Point
Section P.5 Factoring Polynomials
What am I Supposed to learn?
Common Factors
Factoring by Grouping
Factoring Trinomials
Factoring the Difference of Two Squares
Factoring Perfect Square Trinomials
Factoring the Sum or Difference of Two Cubes
A Strategy for Factoring Polynomials
Factoring Algebraic Expressions Containing Fractional and Negative Exponents
CONCEPT AND VOCABULARY CHECK
EXERCISE SET P.5
Practice Exercises
Practice Plus
Application Exercises
Explaining the Concepts
Critical Thinking Exercises
Preview Exercises
Section P.6 Rational Expressions
What am I Supposed to learn?
Rational Expressions
Simplifying Rational Expressions
Multiplying Rational Expressions
Dividing Rational Expressions
Adding and Subtracting Rational Expressions with the Same Denominator
Adding and Subtracting Rational Expressions with Different Denominators
SOLUTION
Check Point 6
SOLUTION
Check Point 7
SOLUTION
Check Point 8
SOLUTION
Check Point 9
Complex Rational Expressions
CONCEPT AND VOCABULARY CHECK
EXERCISE SET P.6
Practice Exercises
Practice Plus
Application Exercises
Explaining the Concepts
Critical Thinking Exercises
Preview Exercises
CHAPTER P Summary, Review, and Test
SUMMARY: BASIC FORMULAS
REVIEW EXERCISES
P.1
P.2
P.3
P.4
P.5
P.6
CHAPTER P TEST
CHAPTER 1 Equations and Inequalities
Section 1.1 Graphs and Graphing Utilities
What am I Supposed to learn?
Points and Ordered Pairs
Graphs of Equations
Graphing Equations and Creating Tables Using a Graphing Utility
Intercepts
Interpreting Information Given by Graphs
CONCEPT AND VOCABULARY CHECK
EXERCISE SET 1.1
Practice Exercises
Practice Plus
Application Exercises
Explaining the Concepts
Technology Exercise
Critical Thinking Exercises
Preview Exercises
Section 1.2 Linear Equations and Rational Equations
What am I Supposed to learn?
Solving Linear Equations in One Variable
Linear Equations with Fractions
Rational Equations
Types of Equations
Applications
CONCEPT AND VOCABULARY CHECK
EXERCISE SET 1.2
Practice Exercises
Practice Plus
Application Exercises
Explaining the Concepts
Technology Exercises
Critical Thinking Exercises
Preview Exercises
Section 1.3 Models and applications
What am I Supposed to learn?
Problem Solving with Linear Equations
Solving a Formula for One of Its Variables
CONCEPT AND VOCABULARY CHECK
EXERCISE SET 1.3
Practice and Application Exercises
Explaining the Concepts
Technology Exercises
Critical Thinking Exercises
Group Exercise
Preview Exercises
Section 1.4 Complex numbers
What am I Supposed to learn?
The Imaginary Unit i
Operations with Complex Numbers
Complex Conjugates and division
Roots of Negative Numbers
CONCEPT AND VOCABULARY CHECK
EXERCISE SET 1.4
Practice Exercises
Practice Plus
Application Exercises
Explaining the Concepts
Critical Thinking Exercises
Preview Exercises
Section 1.5 Quadratic Equations
What am I Supposed to learn?
Solving Quadratic Equations by Factoring
Solving Quadratic Equations by the Square Root Property
Completing the Square
Solving Quadratic Equations Using the Quadratic Formula
The Discriminant
Determining Which Method to Use
Applications
CONCEPT AND VOCABULARY CHECK
EXERCISE SET 1.5
Practice Exercises
Practice Plus
Application Exercises
Explaining the Concepts
Technology Exercises
Critical Thinking Exercises
Preview Exercises
CHAPTER 1 Mid-Chapter Check Point
Section 1.6 Other Types of Equations
What am I Supposed to learn?
Polynomial Equations
Radical Equations
Equations with Rational Exponents
Equations That Are Quadratic in Form
Equations Involving Absolute Value
Applications
CONCEPT AND VOCABULARY CHECK
EXERCISE SET 1.6
Practice Exercises
Practice Plus
Application Exercises
Explaining the Concepts
Technology Exercises
Critical Thinking Exercises
Preview Exercises
Section 1.7 Linear Inequalities and Absolute Value Inequalities
What am I Supposed to learn?
Interval Notation
Intersections and Unions of Intervals
Solving Linear Inequalities in One Variable
Inequalities with Unusual Solution Sets
Solving Compound Inequalities
Solving Inequalities with Absolute Value
Applications
SOLUTION
Check Point 11
CONCEPT AND VOCABULARY CHECK
EXERCISE SET 1.7
Practice Exercises
Practice Plus
Application Exercises
Explaining the Concepts
Technology Exercises
Critical Thinking Exercises
Group Exercise
Preview Exercises
CHAPTER 1 Summary, Review, and Test
SUMMARY
REVIEW EXERCISES
1.1
1.2
1.3
1.4
1.5
1.6
1.7
CHAPTER 1 TEST
CHAPTER 2 Functions and Graphs
Section 2.1 Basics of Functions and Their Graphs
What am I Supposed to learn?
Relations
Functions
Functions as Equations
Function Notation
Graphs of Functions
The Vertical Line Test
Obtaining Information from Graphs
Identifying Domain and Range from a Function’s Graph
Identifying Intercepts from a Function’s Graph
CONCEPT AND VOCABULARY CHECK
EXERCISE SET 2.1
Practice Exercises
Practice Plus
Application Exercises
Explaining the Concepts
Technology Exercise
Critical Thinking Exercises
Retaining the Concepts
Preview Exercises
Section 2.2 More on Functions and Their Graphs
What am I Supposed to learn?
Increasing and Decreasing Functions
Relative Maxima and Relative Minima
Tests for Symmetry
Even and Odd Functions
Piecewise Functions
Functions and Difference Quotients
CONCEPT AND VOCABULARY CHECK
EXERCISE SET 2.2
Practice Exercises
Practice Plus
Application Exercises
Explaining the Concepts
Technology Exercises
Critical Thinking Exercises
Retaining the Concepts
Preview Exercises
Section 2.3 Linear Functions and slope
What am I Supposed to learn?
The slope of a Line
The point-slope Form of the Equation of a Line
The slope-Intercept Form of the Equation of a Line
Equations of Horizontal and Vertical Lines
The General Form of the Equation of a Line
Using Intercepts to Graph Ax+By+C=0
Applications
CONCEPT AND VOCABULARY CHECK
EXERCISE SET 2.3
Practice Exercises
Practice Plus
Application Exercises
Explaining the Concepts
Technology Exercises
Critical Thinking Exercises
Group Exercise
Retaining the Concepts
Preview Exercises
Section 2.4 More on slope
What am I Supposed to learn?
Parallel and Perpendicular Lines
Slope as Rate of Change
The Average Rate of Change of a Function
CONCEPT AND VOCABULARY CHECK
EXERCISE SET 2.4
Practice Exercises
Practice Plus
Application Exercises
Explaining the Concepts
Technology Exercise
Critical Thinking Exercises
Retaining the Concepts
Preview Exercises
CHAPTER 2 Mid-Chapter Check Point
Section 2.5 Transformations of Functions
What am I Supposed to learn?
Graphs of Common Functions
Vertical shifts
Horizontal Shifts
Reflections of Graphs
Vertical stretching and shrinking
Horizontal Stretching and Shrinking
Sequences of Transformations
CONCEPT AND VOCABULARY CHECK
EXERCISE SET 2.5
Practice Exercises
Practice Plus
Application Exercises
Explaining the Concepts
Technology Exercises
Critical Thinking Exercises
Retaining the Concepts
Preview Exercises
Section 2.6 Combinations of Functions; Composite Functions
What am I Supposed to learn?
The Domain of a Function
The Algebra of Functions
Composite Functions
Decomposing Functions
CONCEPT AND VOCABULARY CHECK
EXERCISE SET 2.6
Practice Exercises
Practice Plus
Application Exercises
Explaining the Concepts
Technology Exercises
Critical Thinking Exercises
Retaining the Concepts
Preview Exercises
Section 2.7 Inverse Functions
What am I Supposed to learn?
Inverse Functions
Finding the inverse of a Function
The horizontal line Test and One-to-One Functions
Graphs of f and f−1
CONCEPT AND VOCABULARY CHECK
EXERCISE SET 2.7
Practice Exercises
Practice Plus
Application Exercises
Explaining the Concepts
Technology Exercises
Critical Thinking Exercises
Group Exercise
Retaining the Concepts
Preview Exercises
Section 2.8 Distance and Midpoint Formulas; Circles
What am I Supposed to learn?
The Distance Formula
The Midpoint Formula
Circles
CONCEPT AND VOCABULARY CHECK
EXERCISE SET 2.8
Practice Exercises
Practice Plus
Application Exercises
Explaining the Concepts
Technology Exercises
Critical Thinking Exercises
Retaining the Concepts
Preview Exercises
CHAPTER 2 Summary, Review, and Test
SUMMARY
REVIEW EXERCISES
2.1 and 2.2
2.3 and 2.4
2.5
2.6
2.7
2.8
CHAPTER 2 TEST
CUMULATIVE REVIEW EXERCISES (CHAPTERS 1–2)
CHAPTER 3 Polynomial and Rational Functions
Section 3.1 Quadratic Functions
What am I supposed to learn?
Graphs of Quadratic Functions
Graphing Quadratic Functions in Standard Form
Graphing Quadratic Functions in the Form f(x)=ax2+bx+c
SOLUTION
Check Point 3
Minimum and Maximum Values of Quadratic Functions
Applications of Quadratic Functions
CONCEPT AND VOCABULARY CHECK
EXERCISE SET 3.1
Practice Exercises
Practice Plus
Application Exercises
Explaining the Concepts
Technology Exercises
Critical Thinking Exercises
Group Exercise
Retaining the Concepts
Preview Exercises
Section 3.2 Polynomial Functions and Their Graphs
What am I Supposed to learn?
Smooth, Continuous Graphs
End Behavior of Polynomial Functions
Zeros of Polynomial Functions
Multiplicities of Zeros
The Intermediate Value Theorem
Turning Points of Polynomial Functions
A Strategy for Graphing Polynomial Functions
CONCEPT AND VOCABULARY CHECK
EXERCISE SET 3.2
Practice Exercises
Practice Plus
Application Exercises
Explaining the Concepts
Technology Exercises
Critical Thinking Exercises
Retaining the Concepts
Preview Exercises
Section 3.3 Dividing Polynomials; Remainder and Factor Theorems
What am I Supposed to learn?
Long Division of Polynomials and the Division Algorithm
Dividing Polynomials Using Synthetic Division
The Remainder Theorem
The Factor Theorem
CONCEPT AND VOCABULARY CHECK
EXERCISE SET 3.3
Practice Exercises
Practice Plus
Application Exercises
Explaining the Concepts
Technology Exercise
Critical Thinking Exercises
Retaining the Concepts
Preview Exercises
Section 3.4 Zeros of Polynomial Functions
What am I Supposed to learn?
The Rational Zero Theorem
The Fundamental Theorem of Algebra
The Linear Factorization Theorem
Descartes’s Rule of Signs
CONCEPT AND VOCABULARY CHECK
EXERCISE SET 3.4
Practice Exercises
Practice Plus
Application Exercises
Explaining the Concepts
Technology Exercises
Critical Thinking Exercises
Retaining the Concepts
Preview Exercises
CHAPTER 3 Mid-Chapter Check Point
Section 3.5 Rational Functions and Their Graphs
What am I Supposed to learn?
Rational Functions
Vertical Asymptotes of Rational Functions
Horizontal Asymptotes of Rational Functions
Using Transformations to Graph Rational Functions
Graphing Rational Functions
Slant Asymptotes
Applications
CONCEPT AND VOCABULARY CHECK
EXERCISE SET 3.5
Practice Exercises
Practice Plus
Application Exercises
Explaining the Concepts
Technology Exercises
Critical Thinking Exercises
Retaining the Concepts
Preview Exercises
Section 3.6 Polynomial and Rational Inequalities
What am I Supposed to learn?
Solving Polynomial Inequalities
Solving Rational Inequalities
Applications
CONCEPT AND VOCABULARY CHECK
EXERCISE SET 3.6
Practice Exercises
Practice Plus
Application Exercises
Explaining the Concepts
Technology Exercises
Critical Thinking Exercises
Retaining the Concepts
Preview Exercises
Section 3.7 Modeling Using Variation
What am I Supposed to learn?
Direct Variation
Inverse Variation
Combined Variation
Joint Variation
CONCEPT AND VOCABULARY CHECK
EXERCISE SET 3.7
Practice Exercises
Practice Plus
Application Exercises
Explaining the Concepts
Technology Exercise
Critical Thinking Exercises
Group Exercise
Retaining the Concepts
Preview Exercises
CHAPTER 3 Summary, Review, and Test
SUMMARY
REVIEW EXERCISES
3.1
3.2
3.3
3.4
3.5
3.6
3.7
CHAPTER 3 TEST
CUMULATIVE REVIEW EXERCISES (CHAPTERS 1–3)
CHAPTER 4 Exponential and Logarithmic Functions
Section 4.1 Exponential Functions
What am I Supposed to learn?
Graphing Exponential Functions
Transformations of Exponential Functions
SOLUTION
Check Point 4
SOLUTION
Check Point 5
The Natural Base e
Compound Interest
CONCEPT AND VOCABULARY CHECK
EXERCISE SET 4.1
Practice Exercises
Practice Plus
Application Exercises
Explaining the Concepts
Technology Exercises
Critical Thinking Exercises
Retaining the Concepts
Preview Exercises
Section 4.2 Logarithmic Functions
What am I Supposed to learn?
The Definition of Logarithmic Functions
Basic Logarithmic Properties
Graphs of Logarithmic Functions
The Domain of a Logarithmic Function
Common Logarithms
Natural Logarithms
CONCEPT AND VOCABULARY CHECK
EXERCISE SET 4.2
Practice Exercises
Practice Plus
Application Exercises
Explaining the Concepts
Technology Exercises
Critical Thinking Exercises
Group Exercise
Retaining the Concepts
Preview Exercises
Section 4.3 Properties of Logarithms
What am I Supposed to learn?
The Product Rule
The Quotient Rule
The Power Rule
Expanding logarithmic Expressions
Condensing Logarithmic Expressions
The Change-of-Base property
CONCEPT AND VOCABULARY CHECK
EXERCISE SET 4.3
Practice Exercises
Practice Plus
Application Exercises
Explaining the Concepts
Technology Exercises
Critical Thinking Exercises
Retaining the Concepts
Preview Exercises
CHAPTER 4 Mid-Chapter Check Point
Section 4.4 Exponential and Logarithmic Equations
What am I Supposed to learn?
Exponential Equations
Logarithmic Equations
Applications
SOLUTION
Check Point 9
SOLUTION
Check Point 10
SOLUTION
Check Point 11
CONCEPT AND VOCABULARY CHECK
EXERCISE SET 4.4
Practice Exercises
Practice Plus
Application Exercises
Explaining the Concepts
Technology Exercises
Critical Thinking Exercises
Group Exercise
Retaining the Concepts
Preview Exercises
Section 4.5 Exponential Growth and Decay; Modeling Data
What am I Supposed to learn?
Exponential Growth and Decay
Logistic Growth Models
Modeling Data
Expressing y=abx in Base e
CONCEPT AND VOCABULARY CHECK
EXERCISE SET 4.5
Practice Exercises and Application Exercises
Explaining the Concepts
Technology Exercises
Critical Thinking Exercises
Group Exercise
Retaining the Concepts
Preview Exercises
CHAPTER 4 Summary, Review, and Test
SUMMARY
REVIEW EXERCISES
4.1
4.2
4.3
4.4
4.5
CHAPTER 4 TEST
CUMULATIVE REVIEW EXERCISES (CHAPTERS 1–4)
CHAPTER 5 Systems of Equations and Inequalities
Section 5.1 Systems of Linear Equations in Two Variables
What am I Supposed to learn?
Systems of Linear Equations and Their Solutions
Eliminating a Variable Using the Substitution Method
Eliminating a Variable Using the Addition Method
Linear Systems Having No Solution or Infinitely Many Solutions
Functions of Business: Break-Even Analysis
Problems Involving Mixtures
SOLUTION
Check Point 8
CONCEPT AND VOCABULARY CHECK
EXERCISE SET 5.1
Practice Exercises
Practice Plus
Application Exercises
Explaining the Concepts
Technology Exercise
Critical Thinking Exercises
Group Exercise
Retaining the Concepts
Preview Exercises
Section 5.2 Systems of Linear Equations in Three Variables
What am I Supposed to learn?
Systems of Linear Equations in Three Variables and Their Solutions
Solving Systems of Linear Equations in Three Variables by Eliminating Variables
Applications
CONCEPT AND VOCABULARY CHECK
EXERCISE SET 5.2
Practice Exercises
Practice Plus
Application Exercises
Explaining the Concepts
Technology Exercises
Critical Thinking Exercises
Group Exercise
Retaining the Concepts
Preview Exercises
Section 5.3 Partial Fractions
What am I Supposed to learn?
The Idea behind Partial Fraction Decomposition
The Partial Fraction decomposition of a rational Expression with Distinct Linear Factors in the denominator
The Partial Fraction Decomposition of a Rational Expression with Linear Factors in the denominator, Some of Which Are repeated
The Partial Fraction Decomposition of a Rational Expression with Prime, Nonrepeated Quadratic Factors in the Denominator
The Partial Fraction Decomposition of a Rational Expression with a Prime, repeated Quadratic Factor in the Denominator
CONCEPT AND VOCABULARY CHECK
EXERCISE SET 5.3
Practice Exercises
Practice Plus
Application Exercises
Explaining the Concepts
Technology Exercise
Critical Thinking Exercises
Retaining the Concepts
Preview Exercises
Section 5.4 Systems of Nonlinear Equations in Two Variables
What am I Supposed to learn?
Systems of Nonlinear Equations and Their Solutions
Eliminating a Variable Using the Substitution Method
Eliminating a Variable Using the Addition Method
Applications
CONCEPT AND VOCABULARY CHECK
EXERCISE SET 5.4
Practice Exercises
Practice Plus
Application Exercises
Explaining the Concepts
Technology Exercises
Critical Thinking Exercises
Retaining the Concepts
Preview Exercises
CHAPTER 5 Mid-Chapter Check Point
Section 5.5 Systems of Inequalities
What am I Supposed to learn?
Linear Inequalities in Two Variables and Their Solutions
The Graph of a Linear Inequality in Two Variables
Graphing Linear Inequalities without Using Test Points
SOLUTION
Check Point 3
Graphing a Nonlinear Inequality in Two Variables
Modeling with Systems of Linear Inequalities
Graphing Systems of Linear Inequalities
CONCEPT AND VOCABULARY CHECK
EXERCISE SET 5.5
Practice Exercises
Practice Plus
Application Exercises
Explaining the Concepts
Technology Exercises
Critical Thinking Exercises
Retaining the Concepts
Preview Exercises
Section 5.6 Linear Programming
What am I Supposed to learn?
Objective Functions in Linear Programming
Constraints in Linear Programming
Solving Problems with Linear Programming
CONCEPT AND VOCABULARY CHECK
EXERCISE SET 5.6
Practice Exercises
Application Exercises
Explaining the Concepts
Critical Thinking Exercises
Group Exercises
Retaining the Concepts
Preview Exercises
CHAPTER 5 Summary, Review, and Test
SUMMARY
REVIEW EXERCISES
5.1
5.2
5.3
5.4
5.5
5.6
CHAPTER 5 TEST
CUMULATIVE REVIEW EXERCISES (CHAPTERS 1–5)
CHAPTER 6 Matrices and Determinants
Section 6.1 Matrix Solutions to Linear Systems
What am I Supposed to learn?
Augmented Matrices
Matrix Row Operations
Solving Linear Systems Using Gaussian Elimination
Solving Linear Systems Using Gauss-Jordan Elimination
TECHNOLOGY
SOLUTION
Check Point 5
CONCEPT AND VOCABULARY CHECK
EXERCISE SET 6.1
Practice Exercises
Practice Plus
Application Exercises
Explaining the Concepts
Technology Exercises
Critical Thinking Exercises
Retaining the Concepts
Preview Exercises
Section 6.2 Inconsistent and Dependent Systems and Their Applications
What am I Supposed to learn?
Nonsquare Systems
Applications
CONCEPT AND VOCABULARY CHECK
EXERCISE SET 6.2
Practice Exercises
Practice Plus
Application Exercises
Explaining the Concepts
Technology Exercise
Critical Thinking Exercises
Group Exercise
Retaining the Concepts
Preview Exercises
Section 6.3 Matrix Operations and Their Applications
What am I Supposed to learn?
Notations for Matrices
Equality of Matrices
Matrix Addition and Subtraction
Scalar Multiplication
Matrix Multiplication
Applications
CONCEPT AND VOCABULARY CHECK
EXERCISE SET 6.3
Practice Exercises
Practice Plus
Application Exercises
Explaining the Concepts
Technology Exercise
Critical Thinking Exercises
Group Exercise
Retaining the Concepts
Preview Exercises
CHAPTER 6 Mid-Chapter Check Point
Section 6.4 Multiplicative Inverses of Matrices and Matrix Equations
What am I Supposed to learn?
The Multiplicative Identity Matrix
The Multiplicative Inverse of a Matrix
A Quick Method for Finding the Multiplicative Inverse of a 2×2 Matrix
SOLUTION
Check Point 3
Finding Multiplicative Inverses of n×n Matrices with n Greater Than 2
SOLUTION
Check Point 4
Solving Systems of Equations Using Multiplicative Inverses of Matrices
Applications of Matrix Inverses to Coding
CONCEPT AND VOCABULARY CHECK
EXERCISE SET 6.4
Practice Exercises
Practice Plus
Application Exercises
Explaining the Concepts
Technology Exercises
Critical Thinking Exercises
Group Exercise
Retaining the Concepts
Preview Exercises
Section 6.5 Determinants and Cramer’s Rule
What am I Supposed to learn?
The Determinant of a 2 × 2 Matrix
Solving Systems of Linear Equations in Two Variables Using Determinants
The Determinant of a 3 × 3 Matrix
Solving Systems of Linear Equations in Three Variables Using Determinants
The Determinant of Any n × n Matrix
CONCEPT AND VOCABULARY CHECK
EXERCISE SET 6.5
Practice Exercises
Practice Plus
Application Exercises
Explaining the Concepts
Technology Exercises
Critical Thinking Exercises
Group Exercise
Retaining the Concepts
Preview Exercises
CHAPTER 6 Summary, Review, and Test
SUMMARY
REVIEW EXERCISES
6.1
6.2
6.3
6.4
6.5
CHAPTER 6 TEST
CUMULATIVE REVIEW EXERCISES (CHAPTERS 1–6)
CHAPTER 7 Conic Sections
Section 7.1 The Ellipse
What am I Supposed to learn?
Definition of an Ellipse
Standard Form of the Equation of an Ellipse
Using the Standard Form of the Equation of an Ellipse
Translations of Ellipses
Applications
CONCEPT AND VOCABULARY CHECK
EXERCISE SET 7.1
Practice Exercises
Practice Plus
Application Exercises
Explaining the Concepts
Technology Exercises
Critical Thinking Exercises
Retaining the Concepts
Preview Exercises
Section 7.2 The Hyperbola
What am I Supposed to learn?
Definition of a Hyperbola
Standard Form of the Equation of a Hyperbola
Using the Standard Form of the Equation of a Hyperbola
The Asymptotes of a Hyperbola
Graphing Hyperbolas Centered at the Origin
Translations of Hyperbolas
Applications
CONCEPT AND VOCABULARY CHECK
EXERCISE SET 7.2
Practice Exercises
Practice Plus
Application Exercises
Explaining the Concepts
Technology Exercises
Critical Thinking Exercises
Retaining the Concepts
Preview Exercises
CHAPTER 7 Mid-Chapter Check Point
Section 7.3 The Parabola
What am I Supposed to learn?
Definition of a Parabola
Standard Form of the Equation of a Parabola
Using the Standard Form of the Equation of a Parabola
Translations of Parabolas
Applications
Degenerate Conic Sections
Identifying Conic Sections without Completing the Square
CONCEPT AND VOCABULARY CHECK
EXERCISE SET 7.3
Practice Exercises
Practice Plus
Application Exercises
Explaining the Concepts
Technology Exercises
Critical Thinking Exercises
Group Exercise
Retaining the Concepts
Preview Exercises
CHAPTER 7 Summary, Review, and Test
SUMMARY
REVIEW EXERCISES
7.1
7.2
7.3
CHAPTER 7 TEST
CUMULATIVE REVIEW EXERCISES (CHAPTERS 1–7)
CHAPTER 8 Sequences, Induction, and Probability
Section 8.1 Sequences and Summation Notation
What am I Supposed to learn?
Sequences
Recursion Formulas
Factorial Notation
Summation Notation
CONCEPT AND VOCABULARY CHECK
EXERCISE SET 8.1
Practice Exercises
Practice Plus
Application Exercises
Explaining the Concepts
Technology Exercises
Critical Thinking Exercises
Group Exercise
Retaining the Concepts
Preview Exercises
Section 8.2 Arithmetic Sequences
What am I Supposed to learn?
Arithmetic Sequences
The General Term of an Arithmetic Sequence
The Sum of the First n Terms of an Arithmetic Sequence
CONCEPT AND VOCABULARY CHECK
EXERCISE SET 8.2
Practice Exercises
Practice Plus
Application Exercises
Explaining the Concepts
Technology Exercises
Critical Thinking Exercises
Retaining the Concepts
Preview Exercises
Section 8.3 Geometric Sequences and Series
What am I Supposed to learn?
Geometric Sequences
The General Term of a Geometric Sequence
The Sum of the First n Terms of a Geometric Sequence
Annuities
Geometric Series
CONCEPT AND VOCABULARY CHECK
EXERCISE SET 8.3
Practice Exercises
Practice Plus
Application Exercises
Explaining the Concepts
Technology Exercises
Critical Thinking Exercises
Group Exercise
Retaining the Concepts
Preview Exercises
CHAPTER 8 Mid-Chapter Check Point
Section 8.4 Mathematical Induction
What am I Supposed to learn?
The Principle of Mathematical Induction
SOLUTION
Check Point 1
Proving Statements about Positive Integers Using Mathematical Induction
SOLUTION
Check Point 2
SOLUTION
Check Point 3
SOLUTION
Check Point 4
CONCEPT AND VOCABULARY CHECK
EXERCISE SET 8.4
Practice Exercises
Practice Plus
Explaining the Concepts
Critical Thinking Exercises
Group Exercise
Retaining the Concepts
Preview Exercises
Section 8.5 The Binomial Theorem
What am I Supposed to learn?
Binomial Coefficients
The Binomial Theorem
Finding a Particular Term in a Binomial Expansion
CONCEPT AND VOCABULARY CHECK
EXERCISE SET 8.5
Practice Exercises
Practice Plus
Application Exercises
Explaining the Concepts
Technology Exercises
Critical Thinking Exercises
Retaining the Concepts
Preview Exercises
Section 8.6 Counting Principles, Permutations, and Combinations
What am I Supposed to learn?
The Fundamental Counting Principle
Permutations
Section 8.7 Probability
What am I Supposed to learn?
Empirical Probability
Theoretical Probability
Computing Theoretical Probability without Listing an Event and the Sample Space
SOLUTION
Check Point 4
SOLUTION
Check Point 5
Probability of an Event Not Occurring
Or Probabilities with Mutually Exclusive Events
Or Probabilities with Events That Are Not Mutually Exclusive
SOLUTION
Check Point 8
Solution
Check Point 9
And Probabilities with Independent Events
CONCEPT AND VOCABULARY CHECK
EXERCISE SET 8.7
Practice and Application Exercises
Explaining the Concepts
Critical Thinking Exercises
Retaining the Concepts
Group Exercise
CHAPTER 8 Summary, Review, and Test
SUMMARY
REVIEW EXERCISES
8.1
8.2
8.3
8.4
8.5
8.6
8.7
CHAPTER 8 TEST
CUMULATIVE REVIEW EXERCISES (CHAPTERS 1–8)
APPENDIX Where Did That Come From? Selected Proofs
Section 4.3 Properties of Logarithms
The Product Rule
Proof
The Change-of-Base Property
Proof
Section 7.1 The Ellipse
The Standard Form of the Equation of an Ellipse with a Horizontal Major Axis Centered at the Origin
Proof
Section 7.2 The Hyperbola
The Asymptotes of a Hyperbola Centered at the Origin
Proof
ANSWERS TO SELECTED EXERCISES
CHAPTER P
Section P.1
Check Point Exercises
CONCEPT AND VOCABULARY CHECK
EXERCISE SET P.1
Section P.2
Check Point Exercises
CONCEPT AND VOCABULARY CHECK
EXERCISE SET P.2
Section P.3
Check Point Exercises
CONCEPT AND VOCABULARY CHECK
EXERCISE SET P.3
Section P.4
Check Point Exercises
CONCEPT AND VOCABULARY CHECK
EXERCISE SET P.4
Mid-Chapter P Check Point
Section P.5
Check Point Exercises
CONCEPT AND VOCABULARY CHECK
EXERCISE SET P.5
Section P.6
Check Point Exercises
CONCEPT AND VOCABULARY CHECK
Exercise Set P.6
Chapter P Review Exercises
Chapter P Test
CHAPTER 1
Section 1.1
Check Point Exercises
CONCEPT AND VOCABULARY CHECK
EXERCISE SET 1.1
Section 1.2
Check Point Exercises
CONCEPT AND VOCABULARY CHECK
EXERCISE SET 1.2
Section 1.3
Check Point Exercises
CONCEPT AND VOCABULARY CHECK
EXERCISE SET 1.3
Section 1.4
Check Point Exercises
CONCEPT AND VOCABULARY CHECK
EXERCISE SET 1.4
Section 1.5
Check Point Exercises
CONCEPT AND VOCABULARY CHECK
EXERCISE SET 1.5
Mid-Chapter 1 Check Point
Section 1.6
Check Point Exercises
CONCEPT AND VOCABULARY CHECK
EXERCISE SET 1.6
Section 1.7
Check Point Exercises
CONCEPT AND VOCABULARY CHECK
EXERCISE SET 1.7
Chapter 1 Review Exercises
Chapter 1 Test
CHAPTER 2
Section 2.1
Check Point Exercises
CONCEPT AND VOCABULARY CHECK
Exercise Set 2.1
Section 2.2
Check Point Exercises
CONCEPT AND VOCABULARY CHECK
EXERCISE SET 2.2
Section 2.3
Check Point Exercises
CONCEPT AND VOCABULARY CHECK
EXERCISE SET 2.3
Section 2.4
Check Point Exercises
CONCEPT AND VOCABULARY CHECK
EXERCISE SET 2.4
Mid-Chapter 2 Check Point
Section 2.5
Check Point Exercises
CONCEPT AND VOCABULARY CHECK
EXERCISE SET 2.5
Section 2.6
Check Point Exercises
CONCEPT AND VOCABULARY CHECK
EXERCISE SET 2.6
Section 2.7
Check Point Exercises
CONCEPT AND VOCABULARY CHECK
EXERCISE SET 2.7
Section 2.8
Check Point Exercises
CONCEPT AND VOCABULARY CHECK
EXERCISE SET 2.8
Chapter 2 Review Exercises
Chapter 2 Test
Cumulative Review Exercises (Chapters 1–2)
CHAPTER 3
Section 3.1
Check Point Exercises
CONCEPT AND VOCABULARY CHECK
Exercise Set 3.1
Section 3.2
Check Point Exercises
CONCEPT AND VOCABULARY CHECK
EXERCISE SET 3.2
Section 3.3
Check Point Exercises
CONCEPT AND VOCABULARY CHECK
EXERCISE SET 3.3
Section 3.4
Check Point Exercises
CONCEPT AND VOCABULARY CHECK
EXERCISE SET 3.4
Mid-Chapter 3 Check Point
Section 3.5
Check Point Exercises
CONCEPT AND VOCABULARY CHECK
EXERCISE SET 3.5
Section 3.6
Check Point Exercises
CONCEPT AND VOCABULARY CHECK
Exercise Set 3.6
Section 3.7
Check Point Exercises
CONCEPT AND VOCABULARY CHECK
EXERCISE SET 3.7
Chapter 3 Review Exercises
Chapter 3 Test
Cumulative Review Exercises (Chapters 1–3)
CHAPTER 4
Section 4.1
Check Point Exercises
CONCEPT AND VOCABULARY CHECK
EXERCISE SET 4.1
Section 4.2
Check Point Exercises
CONCEPT AND VOCABULARY CHECK
EXERCISE SET 4.2
Section 4.3
Check Point Exercises
CONCEPT AND VOCABULARY CHECK
EXERCISE SET 4.3
Mid-Chapter 4 Check Point
Section 4.4
Check Point Exercises
CONCEPT AND VOCABULARY CHECK
EXERCISE SET 4.4
Section 4.5
Check Point Exercises
CONCEPT AND VOCABULARY CHECK
EXERCISE SET 4.5
Chapter 4 REVIEW EXERCISES
Chapter 4 Test
Cumulative Review Exercises (Chapters 1–4)
CHAPTER 5
Section 5.1
Check Point Exercises
CONCEPT AND VOCABULARY CHECK
EXERCISE SET 5.1
Section 5.2
Check Point Exercises
CONCEPT AND VOCABULARY CHECK
EXERCISE SET 5.2
Section 5.3
Check Point Exercises
CONCEPT AND VOCABULARY CHECK
EXERCISE SET 5.3
Section 5.4
Check Point Exercises
CONCEPT AND VOCABULARY CHECK
EXERCISE SET 5.4
Mid-Chapter 5 Check Point
Section 5.5
Check Point Exercises
CONCEPT AND VOCABULARY CHECK
Exercise Set 5.5
Section 5.6
Check Point Exercises
CONCEPT AND VOCABULARY CHECK
EXERCISE SET 5.6
Chapter 5 Review Exercises
Chapter 5 Test
Cumulative Review Exercises (Chapters 1–5)
Chapter 6
Section 6.1
Check Point Exercises
CONCEPT AND VOCABULARY CHECK
EXERCISE SET 6.1
Section 6.2
Check Point Exercises
CONCEPT AND VOCABULARY CHECK
EXERCISE SET 6.2
Section 6.3
Check Point Exercises
CONCEPT AND VOCABULARY CHECK
EXERCISE SET 6.3
Mid-Chapter 6 Check Point
Section 6.4
Check Point Exercises
CONCEPT AND VOCABULARY CHECK
Exercise Set 6.4
Section 6.5
Check Point Exercises
CONCEPT AND VOCABULARY CHECK
EXERCISE SET 6.5
Chapter 6 Review Exercises
Chapter 6 Test
Cumulative Review Exercises (Chapters 1–6)
Chapter 7
Section 7.1
Check Point Exercises
CONCEPT AND VOCABULARY CHECK
Exercise Set 7.1
Section 7.2
Check Point Exercises
CONCEPT AND VOCABULARY CHECK
EXERCISE SET 7.2
Mid-Chapter 7 Check Point
Section 7.3
Check Point Exercises
CONCEPT AND VOCABULARY CHECK
EXERCISE SET 7.3
Chapter 7 Review Exercises
Chapter 7 Test
Cumulative Review Exercises (Chapters 1–7)
CHAPTER 8
Section 8.1
Check Point Exercises
CONCEPT AND VOCABULARY CHECK
EXERCISE SET 8.1
Section 8.2
Check Point Exercises
CONCEPT AND VOCABULARY CHECK
EXERCISE SET 8.2
Section 8.3
Check Point Exercises
CONCEPT AND VOCABULARY CHECK
EXERCISE SET 8.3
Mid-Chapter 8 Check Point
Section 8.4
Check Point Exercises
CONCEPT AND VOCABULARY CHECK
Exercise Set 8.4
Section 8.5
Check Point Exercises
CONCEPT AND VOCABULARY CHECK
Exercise Set 8.5
Section 8.6
Check Point Exercises
CONCEPT AND VOCABULARY CHECK
EXERCISE SET 8.6
Section 8.7
Check Point Exercises
CONCEPT AND VOCABULARY CHECK
EXERCISE SET 8.7
Chapter 8 Review Exercises
Chapter 8 Test
Cumulative Review Exercises (Chapters 1–8)
CHAPTER P
CHAPTER 1
CHAPTER 2
CHAPTER 3
CHAPTER 4
CHAPTER 5
CHAPTER 6
CHAPTER 7
CHAPTER 8
Definitions, Rules, and Formulas
[Show More]
Preview 11 out of 600 pages