College Algebra plus Integrated Review, 2nd Edition

1.R.1 Exponents, Prime Numbers, and LCM

• Examples
• Example 1: Identifying the Base and Exponent
• Example 3: Evaluating Exponential Expressions
• Example 4: Evaluating Exponential Expressions
• Example 5: Using the Order of Operations with Whole Numbers
• Example 6: Using the Order of Operations with Whole Numbers
• Example 7: Divisibility by 2
• Example 8: Divisibility by 3
• Example 9: Divisibility by 4
• Example 10: Divisibility by 5
• Example 11: Divisibility by 6
• Example 12: Divisibility by 9
• Example 13: Divisibility by 10
• Example 15: Determining Prime Numbers
• Example 16: Determining Composite Numbers
• Example 17: Determining Whether a Number is Prime
• Example 18: Determining Whether a Number is Prime
• Example 20: Finding the Prime Factorization of a Number
• Example 22: Finding the Factors of a Composite Number
• Example 24: Finding the Least Common Multiple (LCM)
• Example 25: Finding the Least Common Multiple (LCM)
• Example 27: Finding the Least Common Multiple (LCM)
• Example 28: Finding the Least Common Multiple (LCM)
• Example 30: Application: Finding the LCM
• Example 31: Finding Equivalent Fractions
• Example 32: Finding Equivalent Fractions

1.R.2 Reducing Fractions to Lowest Terms

• Examples
• Example 1: Reducing Fractions to Lowest Terms
• Example 2: Reducing Fractions to Lowest Terms
• Example 4: Application: Reducing Fractions to Lowest Terms
• Example 5: Multiplying and Reducing Using Prime Factors
• Example 6: Multiplying and Reducing Using Prime Factors
• Example 7: Multiplying and Reducing Using Prime Factors
• Example 9: Application: Multiplying and Reducing Fractions
• Example 10: Multiplying and Reducing Using the Division Method
• Example 11: Multiplying and Reducing Using the Division Method
• Example 12: Multiplying and Reducing Using the Division Method
• Example 13: Multiplying and Reducing Using the Division Method

1.R.3 Decimals and Percents

• Examples
• Example 1: Changing Fractions with Denominators of $100$ to Percents
• Example 2: Changing Decimal Numbers to Percents
• Example 3: Changing Percents to Decimal Numbers
• Example 4: Changing Fractions to Percents
• Example 5: Changing Fractions to Percents
• Example 6: Changing Mixed Numbers to Percents
• Example 8: Changing Fractions to Percents
• Example 9: Application: Changing Fractions to Percents
• Example 10: Changing Percents to Fractions
• Example 11: Changing Percents to Mixed Numbers

1.R.4 Simplifying Radicals

• Examples
• Example 1: Simplifying Radical Expressions with Square Roots
• Example 2: Simplifying Square Roots with Variables
• Example 3: Simplifying Square Roots with Variables
• Example 4: Simplifying Expressions with Cube Roots

1.1 The Real Number System

• Examples
• Example 1: Types of Real Numbers
• Example 2: Drawing the Real Number Line
• Example 3: Working with Order
• Example 4: Set-Builder Notation
• Example 5: Intervals of Real Numbers
• Example 6: Absolute Value
• Example 7: Using Absolute Value Properties
• Example 8: Working With Repeating Digits
• Bonus Videos
• Bonus 1: The Real Number System
• Bonus 2: The Real Number System

1.2 The Arithmetic of Algebraic Expressions

• Examples
• Example 1: Terminology of Algebraic Expressions
• Example 2: Evaluating Algebraic Expressions
• Example 3: Applying the Field Properties
• Example 4: Visualizing the Distributive Property
• Example 5: Properties of Real Numbers
• Example 6: Order of Operations
• Example 7: Union and Intersection of Intervals
• Example 8: Union and Intersection
• Bonus Videos
• Bonus 1: The Arithmetic of Algebraic Expressions

1.3a Properties of Exponents

• Examples
• Example 1: Natural Number Exponents
• Example 2: Simplifying Exponents
• Example 3: Properties of Exponents
• Bonus Videos
• Bonus 1: Properties of Exponents

1.3b Scientific Notation and Geometric Problems Using Exponents

• Examples
• Example 1: Scientific Notation
• Example 2: Simplifying Expressions with Scientific Notation
• Example 3: Geometric Formulas
• Bonus Videos
• Bonus 1: Scientific Notation and Geometric Problems Using Exponents

1.4a Properties of Radicals

• Examples
• Example 1: Radical Notation
• Example 2: The Pythagorean Theorem
• Example 3: Simplifying Radical Expressions
• Example 4: Rationalizing the Denominator
• Example 5: Rationalizing the Numerator
• Bonus Videos
• Bonus 1: Properties of Radicals
• Bonus 2: Properties of Radicals

1.4b Rational Number Exponents

• Examples
• Example 1: Combining Radicals
• Example 2: Simplifying Expressions
• Example 3: Simplifying Radical Expressions
• Example 4: Finding Areas with Heron's Formula
• Bonus Videos
• Bonus 1: Rational Number Exponents
• Bonus 2: Rational Number Exponents

1.5 Polynomials and Factoring

• Examples
• Example 1: Polynomial Expressions
• Example 2: Adding and Subtracting Polynomials
• Example 3: Multiplying Polynomials
• Example 4: The FOIL Method
• Example 5: The Greatest Common Factor Method
• Example 6: Factoring by Grouping
• Example 7: Factoring Special Binomials
• Example 8: Factoring a Trinomial
• Example 9: Factoring a Trinomial by Grouping
• Example 10: Perfect Square Trinomials
• Example 11: Factoring Expressions with Fractional Exponents
• Bonus Videos
• Bonus 1: Polynomials and Factoring
• Bonus 2: Polynomials and Factoring

1.6 The Complex Number System

• Examples
• Example 1: The Number i
• Example 2: Powers of i
• Example 3: Simplifying Complex Expressions
• Example 4: Dividing Complex Numbers
• Example 5: Roots and Complex Numbers
• Bonus Videos
• Bonus 1: The Complex Number System
• Bonus 2: The Complex Number System
• Bonus 3: The Complex Number System
• Bonus 4: The Complex Number System

2.R.1 Multiplication and Division with Fractions

• Examples
• Example 1: Multiplying Fractions
• Example 2: Multiplying Fractions
• Example 3: Application: Multiplying Fractions
• Example 4: Recognizing the Properties of Multiplication
• Example 5: Reducing Fractions to Lowest Terms
• Example 6: Reducing Fractions to Lowest Terms
• Example 8: Application: Reducing Fractions to Lowest Terms
• Example 9: Multiplying and Reducing Using Prime Factors
• Example 10: Multiplying and Reducing Using Prime Factors
• Example 11: Multiplying and Reducing Using Prime Factors
• Example 13: Application: Multiplying and Reducing Fractions
• Example 14: Multiplying and Reducing Using the Division Method
• Example 15: Multiplying and Reducing Using the Division Method
• Example 16: Multiplying and Reducing Using the Division Method
• Example 17: Multiplying and Reducing Using the Division Method
• Example 18: Finding Reciprocals
• Example 19: Finding Reciprocals
• Example 20: Dividing Fractions
• Example 21: Dividing Fractions
• Example 22: Dividing and Reducing Fractions
• Example 23: Dividing and Reducing Fractions
• Example 26: Finding a Missing Number
• Example 27: Application: Dividing Fractions
• Example 28: Application: Multiplying and Dividing Fractions

2.R.2 Addition and Subtraction with Fractions

• Examples
• Example 1: Adding Fractions with the Same Denominator
• Example 2: Finding the Least Common Denominator (LCD)
• Example 3: Adding Fractions with Different Denominators
• Example 4: Adding Fractions with Different Denominators
• Example 5: Adding Three Fractions with Different Denominators
• Example 6: Application: Adding Fractions
• Example 7: Application: Adding Fractions
• Example 8: Subtracting Fractions with the Same Denominator
• Example 9: Subtracting Fractions with Different Denominators
• Example 10: Subtracting Fractions with Different Denominators
• Example 11: Subtracting Fractions with Different Denominators
• Example 12: Application: Subtracting Fractions with Different Denominators

2.R.3 Applications: Number Problems and Consecutive Integers

• Examples
• Example 1: Solving Number Problems
• Example 2: Solving Number Problems
• Example 3: Solving Number Problems
• Example 4: Finding Consecutive Integers
• Example 5: Finding Consecutive Integers
• Example 6: Application: Calculating Living Expenses
• Example 7: Application: Calculating Costs of Purchases

2.R.4 Proportions

• Examples
• Example 1: Verifying Proportions
• Example 3: Solving Proportions
• Example 4: Solving Proportions
• Example 5: Solving Proportions
• Example 6: Solving Proportions
• Example 8: Application: Solving Proportions
• Example 9: Application: Solving Proportions
• Example 10: Application: Solving Proportions
• Example 13: Application: Solving Proportions Written in Medical Notation

2.1a Linear Equations in One Variable

• Examples
• Example 1: Solving Linear Equations in One Variable
• Example 2: Solving Linear Equations in One Variable
• Example 3: Solving Absolute Value Equations
• Example 4: Solving Absolute Value Equations Geometrically
• Bonus Videos
• Bonus 1: Linear Equations in One Variable
• Bonus 2: Linear Equations in One Variable
• Bonus 3: Linear Equations in One Variable
• Bonus 4: Linear Equations in One Variable
• Bonus 5: Linear Equations in One Variable

2.1b Applications of Linear Equations in One Variable

• Examples
• Example 1: Solving Linear Equations for One Variable
• Example 2: Calculating Distance
• Example 3: Calculating Average Interest
• Bonus Videos
• Bonus 1: Applications of Linear Equations in One Variable
• Bonus 2: Applications of Linear Equations in One Variable
• Bonus 3: Applications of Linear Equations in One Variable
• Bonus 4: Applications of Linear Equations in One Variable
• Bonus 5: Applications of Linear Equations in One Variable

2.2 Linear Inequalities in One Variable

• Examples
• Example 1: Multiplying Inequalities by Negative Numbers
• Example 2: Solving Linear Inequalities
• Example 3: Graphing Intervals of Real Numbers
• Example 4: Calculating Final Grades
• Example 5: Compound Linear Inequalities
• Example 6: Absolute Value Inequalities
• Example 7: Translating Inequality Phrases
• Example 8: Applications of Inequalities
• Bonus Videos
• Bonus 1: Linear Inequalities in One Variable
• Bonus 2: Linear Inequalities in One Variable
• Bonus 3: Linear Inequalities in One Variable
• Bonus 4: Linear Inequalities in One Variable

2.3 Quadratic Equations in One Variable

• Examples
• Example 1: Solving Quadratic Equations by Factoring
• Example 2: Perfect Square Quadratic Equations
• Example 3: Completing the Square
• Example 4: Using the Quadratic Formula
• Example 5: The Discriminant
• Example 6: Methods of Solving Quadratic Equations
• Example 7: Gravity Problems
• Bonus Videos
• Bonus 1: Quadratic Equations in One Variable
• Bonus 2: Quadratic Equations in One Variable
• Bonus 3: Quadratic Equations in One Variable
• Bonus 4: Quadratic Equations in One Variable

2.4 Higher Degree Polynomial Equations

• Examples
• Example 1: Quadratic-Like Equations
• Example 2: Solving Equations by Factoring
• Example 3: Solving Equations by Factoring
• Bonus Videos
• Bonus 1: Higher Degree Polynomial Equations
• Bonus 2: Higher Degree Polynomial Equations
• Bonus 3: Higher Degree Polynomial Equations
• Bonus 4: Higher Degree Polynomial Equations

2.5 Rational Expressions and Equations

• Examples
• Example 1: Rational Expressions
• Example 2: Combining Rational Expressions
• Example 3: Combining Rational Expressions
• Example 4: Complex Rational Expressions
• Example 5: Solving Rational Equations
• Example 6: Filling a Pool
• Example 7: Filling a Pool Poorly
• Bonus Videos
• Bonus 1: Rational Expressions and Equations
• Bonus 2: Rational Expressions and Equations
• Bonus 3: Rational Expressions and Equations

2.6 Radical Equations

• Examples
• Example 1: Causing Extraneous Solutions
• Example 2: Radical Equations
• Example 3: Escape Speed
• Example 4: Rational Exponents
• Bonus Videos
• Bonus 1: Radical Equations
• Bonus 2: Radical Equations
• Bonus 3: Radical Equations
• Bonus 4: Radical Equations

3.1 The Cartesian Coordinate System

• Examples
• Example 1: Plotting Points in the Cartesian Coordinate System
• Example 2: Graphing Equations in Two Variables
• Example 3: Using the Distance Formula
• Example 4: Using the Midpoint Formula
• Bonus Videos
• Bonus 1: The Cartesian Coordinate System
• Bonus 2: The Cartesian Coordinate System
• Bonus 3: The Cartesian Coordinate System
• Bonus 4: The Cartesian Coordinate System
• Bonus 5: The Cartesian Coordinate System

3.2 Linear Equations in Two Variables

• Examples
• Example 1: Linear Equations in Two Variables
• Example 2: Finding Intercepts and Graphing Linear Equations
• Example 3: Graphing Horizontal and Vertical Lines
• Bonus Videos
• Bonus 1: Linear Equations in Two Variables
• Bonus 2: Linear Equations in Two Variables
• Bonus 3: Linear Equations in Two Variables

3.3 Forms of Linear Equations

• Examples
• Example 1: Calculating the Slope of a Line
• Example 2: Calculating the Slope of a Line
• Example 3: Slope-Intercept Form of a Line
• Example 4: Slope-Intercept Form of a Line
• Example 5: Point-Slope Form of a Line
• Example 6: Point-Slope Form of a Line
• Bonus Videos
• Bonus 1: Forms of Linear Equations
• Bonus 2: Forms of Linear Equations
• Bonus 3: Forms of Linear Equations
• Bonus 4: Forms of Linear Equations

3.4 Parallel and Perpendicular Lines

• Examples
• Example 1: Finding Equations of Parallel Lines
• Example 2: Finding Equations of Parallel Lines
• Example 3: Identifying a Quadrilateral
• Example 4: Finding Equations of Perpendicular Lines
• Example 5: Finding Equations of Perpendicular Lines
• Example 6: Identifying Parallel and Perpendicular Lines
• Bonus Videos
• Bonus 1: Parallel and Perpendicular Lines
• Bonus 2: Parallel and Perpendicular Lines
• Bonus 3: Parallel and Perpendicular Lines
• Bonus 4: Parallel and Perpendicular Lines

3.5 Linear Inequalities in Two Variables

• Examples
• Example 1: Solving Linear Inequalities
• Example 2: Solving Linear Inequalities
• Example 3: Solving Absolute Value Linear Inequalities
• Example 4: Graphing Regions of Constraint
• Example 5: Orchard Business
• Bonus Videos
• Bonus 1: Linear Inequalities in Two Variables
• Bonus 2: Linear Inequalities in Two Variables

3.6 Introduction to Circles

• Examples
• Example 1: Standard Form of a Circle
• Example 2: Standard Form of a Circle
• Example 3: Standard Form of a Circle
• Example 4: Graphing Circles
• Example 5: Graphing Circles and Completing the Square
• Bonus Videos
• Bonus 1: Introduction to Circles
• Bonus 2: Introduction to Circles
• Bonus 3: Introduction to Circles

4.R.1 Order of Operations with Real Numbers

• Examples
• Example 1: Using the Order of Operations with Real Numbers
• Example 2: Using the Order of Operations with Real Numbers
• Example 3: Using the Order of Operations with Real Numbers
• Example 4: Using the Order of Operations with Real Numbers
• Example 6: Using the Order of Operations with Real Numbers
• Example 7: Using the Order of Operations with Real Numbers

4.R.2 Identifying Like Terms

• Examples
• Example 1: Identifying Like Terms

4.R.3 Simplifying Expressions

• Examples
• Example 1: Combining Like Terms

4.R.4 Translating English Phrases and Algebraic Expressions

• Examples
• Example 1: Translating English Phrases into Algebraic Expressions
• Example 2: Application: Translating English Phrases
• Example 3: Translating Algebraic Expressions to English Phrases
• Example 4: Translating Equations into Word Problems

4.1 Relations and Functions

• Examples
• Example 1: Relations, Domains, and Ranges
• Example 2: Is the Relation a Function?
• Example 3: Functions and the Vertical Line Test
• Example 4: Functional Notation
• Example 5: Evaluating Functions
• Example 6: Implied Domain of a Function
• Bonus Videos
• Bonus 1: Relations and Functions
• Bonus 2: Relations and Functions
• Bonus 3: Relations and Functions
• Bonus 4: Relations and Functions
• Bonus 5: Relations and Functions
• Bonus 6: Relations and Functions

4.2a Linear and Quadratic Functions

• Examples
• Example 1: Graphing Linear Functions
• Example 2: Graphing Quadratic Functions
• Example 3: Using the Vertex Formula
• Bonus Videos
• Bonus 1: Linear and Quadratic Functions
• Bonus 2: Linear and Quadratic Functions
• Bonus 3: Linear and Quadratic Functions
• Bonus 4: Linear and Quadratic Functions

4.2b Max/Min Applications of Quadratic Functions

• Examples
• Example 1: Fencing a Garden
• Bonus Videos
• Bonus 1: Max/Min Applications of Quadratic Functions
• Bonus 2: Max/Min Applications of Quadratic Functions
• Bonus 3: Max/Min Applications of Quadratic Functions
• Bonus 4: Max/Min Applications of Quadratic Functions

4.3a Other Common Functions

• Examples
• Example 1: Functions of the Form axⁿ
• Example 2: Functions of the Form ${\displaystyle \frac{a}{x^n}}$
• Example 3: The Absolute Value Function
• Example 4: Piecewise-Defined Function
• Bonus Videos
• Bonus 1: Other Common Functions
• Bonus 2: Other Common Functions
• Bonus 3: Other Common Functions
• Bonus 4: Other Common Functions

4.3b Direct and Inverse Variation

• Examples
• Example 1: Weight in Flight
• Example 2: Spring Scale
• Bonus Videos
• Bonus 1: Direct and Inverse Variation

4.4 Transformations of Functions

• Examples
• Example 1: Horizontal Shifting/Translation
• Example 3: Horizontal and Vertical Shifting
• Example 5: Vertical Stretching and Compressing
• Example 6: Order of Transformations
• Example 7: Symmetry of Equations
• Example 8
• Example 9
• Bonus Videos
• Bonus 1: Transformations of Functions
• Bonus 2: Transformations of Functions
• Bonus 3: Transformations of Functions
• Bonus 4: Transformations of Functions

4.5 Combining Functions

• Examples
• Example 1: Combining Functions Arithmetically
• Example 2: Combining Functions Arithmetically
• Example 3: Combining Functions Arithmetically
• Example 4: Composing Functions
• Example 5: Domains of Compositions of Functions
• Example 6: Domains of Compositions of Functions
• Example 7: Decomposing Functions
• Bonus Videos
• Bonus 1: Combining Functions
• Bonus 2: Combining Functions
• Bonus 3: Combining Functions
• Bonus 4: Combining Functions

4.6 Inverses of Functions

• Examples
• Example 1: Finding the Inverse of a Relation
• Example 2: Inverse Functions
• Example 3: Finding Formulas of Inverse Functions
• Bonus Videos
• Bonus 1: Inverses of Functions
• Bonus 2: Inverses of Functions
• Bonus 3: Inverses of Functions
• Bonus 4: Inverses of Functions

5.R.1 Greatest Common Factor (GCF) of a Set of Terms

• Examples
• Example 1: Finding the GCF

5.R.2 Factoring Trinomials by Grouping

• Examples
• Example 1: Using the ac-Method
• Example 2: Using the ac-Method
• Example 3: Using the ac-Method

5.R.3 Review of Factoring Techniques

5.1 Introduction to Polynomial Equations and Graphs

• Examples
• Example 1: Solutions of Polynomial Equations
• Example 2: Graphing Polynomial Functions
• Example 3: Solving Polynomial Inequalities Using a Graph
• Example 4: Solving Polynomial Inequalities: Sign-Test Method
• Bonus Videos
• Bonus 1: Introduction to Polynomial Equations and Graphs
• Bonus 2: Introduction to Polynomial Equations and Graphs
• Bonus 3: Introduction to Polynomial Equations and Graphs

5.2 Polynomial Division and the Division Algorithm

• Examples
• Example 1: Polynomial Long Division
• Example 2: Polynomial Long Division
• Example 3: Polynomial Long Division with Complex Numbers
• Example 4: Synthetic Division
• Example 5: Synthetic Division (with Complex Numbers)
• Example 6: Constructing Polynomials
• Bonus Videos
• Bonus 1: Polynomial Division and the Division Algorithm
• Bonus 2: Polynomial Division and the Division Algorithm

5.3 Locating Real Zeros of Polynomials

• Examples
• Example 1: The Rational Zero Theorem
• Example 2: Descartes' Rule of Signs
• Example 3: Finding Bounds of Real Zeros
• Example 4: Finding the Zeros of a Polynomial
• Example 5: Intermediate Value Theorem
• Bonus Videos
• Bonus 1: Locating Real Zeros of Polynomials
• Bonus 2: Locating Real Zeros of Polynomials

5.4 The Fundamental Theorem of Algebra

• Examples
• Example 1: Graphing Polynomial Functions
• Example 2: Factoring Polynomials
• Example 3: Constructing Polynomials
• Bonus Videos
• Bonus 1: The Fundamental Theorem of Algebra
• Bonus 2: The Fundamental Theorem of Algebra
• Bonus 3: The Fundamental Theorem of Algebra

6.R.1 Introduction to Rational Expressions

• Examples
• Example 1: Finding Restrictions on the Variable
• Example 2: Evaluating Rational Expressions
• Example 3: Reducing Rational Expressions

6.R.2 Special Products of Binomials

• Examples
• Example 1: Difference of Two Squares
• Example 3: Squares of Binomials

6.R.3 Special Factoring Techniques

• Examples
• Example 1: Factoring the Difference of Two Squares
• Example 2: Factoring the Sum of Two Squares (Not Factorable)
• Example 3: Factoring Perfect Square Trinomials

6.1a Rational Functions

• Examples
• Example 1: Vertical Asymptotes
• Example 2: Horizontal and Oblique Asymptotes
• Example 3: Graphing Rational Functions
• Bonus Videos
• Bonus 1: Rational Functions
• Bonus 2: Rational Functions

6.1b Rational Inequalities

• Examples
• Example 1: Solving Rational Inequalities
• Example 2: Rational Inequalities
• Bonus Videos
• Bonus 1: Rational Inequalities
• Bonus 2: Rational Inequalities

6.2 The Ellipse

• Examples
• Example 1: Graphing an Ellipse Centered at the Origin
• Example 2: Graphing an Ellipse in Standard Form
• Example 3: Graphing an Ellipse Not in Standard Form
• Example 4: Constructing the Equation for an Ellipse
• Bonus Videos
• Bonus 1: The Ellipse

6.3 The Parabola

• Examples
• Example 1: Graphing a Parabola in Standard Form
• Example 2: Graphing a Parabola Not in Standard Form
• Example 3: Standard Form of a Parabola
• Example 4: Parabolic Mirrors
• Bonus Videos
• Bonus 1: The Parabola

6.4 The Hyperbola

• Examples
• Example 1: Graphing a Hyperbola in Standard Form
• Example 2: Graphing a Hyperbola Not in Standard Form
• Example 3: Standard Form of a Hyperbola
• Example 4: LORAN
• Bonus Videos
• Bonus 1: The Hyperbola

7.R.1 Rules for Exponents

• Examples
• Example 1: Using the Product Rule for Exponents
• Example 2: Using the Product Rule for Exponents
• Example 3: Evaluating the Exponent 0
• Example 4: Using the Quotient Rule for Exponents
• Example 5: Dividing Terms with Coefficients
• Example 6: Negative Exponents
• Example 7: Combining Rules for Exponents

7.R.2 Power Rules for Exponents

• Examples
• Example 1: Using the Power Rule for Exponents
• Example 2: Using the Rule for Power of a Product
• Example 3: Using the Rule for Power of a Quotient
• Example 4: Using Combinations of Rules for Exponents
• Example 5: Using Two Approaches with Fractional Expressions and Negative Exponents
• Example 6: Simplifying a More Complex Example

7.R.3 Rational Exponents

• Examples
• Example 1: Evaluating $n^{\mathrm{th}}$ Roots
• Example 2: Converting from Exponential Notation to Radical Notation
• Example 3: Simplifying Expressions with Rational Exponents
• Example 4: Simplifying Radical Notation by Changing to Exponential Notation

7.1 Exponential Functions and Their Graphs

• Examples
• Example 1: Graphing Exponential Functions
• Example 2: Graphing Exponential Functions
• Example 3: Solving Elementary Exponential Equations
• Bonus Videos
• Bonus 1: Exponential Functions and Their Graphs
• Bonus 2: Exponential Functions and Their Graphs
• Bonus 3: Exponential Functions and Their Graphs

7.2 Applications of Exponential Functions

• Examples
• Example 1: Population Growth
• Example 2: Radioactive Decay
• Example 3: Compound Interest Formula
• Example 4: Compound Interest Formula
• Example 5: Continuous Compounding Formula
• Bonus Videos
• Bonus 1: Applications of Exponential Functions
• Bonus 2: Applications of Exponential Functions
• Bonus 3: Applications of Exponential Functions

7.3 Logarithmic Functions and Their Graphs

• Examples
• Example 1: Exponential and Logarithmic Equations
• Example 2: Graphing Logarithmic Functions
• Example 3: Graphing Logarithmic Functions
• Example 4: Logarithmic Expressions
• Example 5: Solving Logarithmic Equations
• Example 6: Evaluating Logarithmic Expressions
• Bonus Videos
• Bonus 1: Logarithmic Functions and Their Graphs
• Bonus 2: Logarithmic Functions and Their Graphs
• Bonus 3: Logarithmic Functions and Their Graphs

7.4 Properties and Applications of Logarithms

• Examples
• Example 1: Continuously Compounded Interest
• Example 2: Solving Exponential Equations
• Example 3: Expanding Logarithmic Expressions
• Example 4: Condensing Logarithmic Expressions
• Example 5: Change of Base Formula
• Example 6: The pH Scale
• Example 7: The Richter Scale
• Example 8: The Decibel Scale
• Bonus Videos
• Bonus 1: Properties and Applications of Logarithms
• Bonus 2: Properties and Applications of Logarithms
• Bonus 3: Properties and Applications of Logarithms

7.5 Exponential and Logarithmic Equations

• Examples
• Example 1: Solving Exponential Equations
• Example 2: Solving Exponential Equations
• Example 3: Solving Logarithmic Equations
• Example 4: Solving Logarithmic Equations
• Example 5: Compounding Interest
• Example 6: Radiocarbon Dating
• Bonus Videos
• Bonus 1: Exponential and Logarithmic Equations
• Bonus 2: Exponential and Logarithmic Equations
• Bonus 3: Exponential and Logarithmic Equations
• Bonus 4: Exponential and Logarithmic Equations
• Bonus 5: Exponential and Logarithmic Equations

8.R.1 Systems of Linear Equations: Solutions by Graphing

• Examples
• Example 1: Checking Solutions to Systems (Solution)
• Example 2: Checking Solutions to Systems (Not a Solution)
• Example 3: Solving Systems (One Solution/A Consistent System)
• Example 4: Solving Systems (No Solution/An Inconsistent System)
• Example 5: Solving Systems (Infinite Solutions/A Dependent System)
• Example 6: Solving a System that Requires Estimation

8.R.2 Systems of Linear Inequalities

• Examples
• Example 1: Solving Systems of Linear Inequalities
• Example 2: Solving Systems of Linear Inequalities
• Example 3: Solving Systems of Linear Inequalities

8.1 Solving Systems by Substitution and Elimination

• Examples
• Example 1: Solving a System of Equations by Substitution
• Example 2: Solving a System of Equations by Substitution
• Example 3: Solving a System of Equations by Elimination
• Example 4: Solving a System of Equations by Elimination
• Example 5: Solving a System of Equations by Elimination
• Example 6: Solving a System of Equations by Elimination
• Example 7: Mixing Alloys
• Example 8: Determining Ages
• Bonus Videos
• Bonus 1: Solving Systems by Substitution and Elimination
• Bonus 2: Solving Systems by Substitution and Elimination

8.2 Matrix Notation and Gaussian Elimination

• Examples
• Example 1: Matrices and Matrix Notation
• Example 2: Augmented Matrices
• Example 3: Row Echelon Form
• Example 4: Elementary Row Operations
• Example 5: Gaussian Elimination
• Example 6: Reduced Row Echelon Form
• Bonus Videos
• Bonus 1: Matrix Notation and Gaussian Elimination
• Bonus 2: Matrix Notation and Gaussian Elimination

8.3 Determinants and Cramer's Rule

• Examples
• Example 1: Determinant of a 2×2 Matrix
• Example 2: Minors and Cofactors
• Example 3: Determinant of an n×n Matrix
• Example 4: Properties of Determinants
• Example 5: Cramer's Rule
• Example 6: Cramer's Rule
• Bonus Videos
• Bonus 1: Determinants and Cramer's Rule

8.4 The Algebra of Matrices

• Examples
• Example 1: Matrix Addition
• Example 2: Matrix Equations
• Example 3: Scalar Multiplication
• Example 4: Matrix Subtraction
• Example 5: Matrix Multiplication
• Example 6: Matrix Multiplication
• Bonus Videos
• Bonus 1: The Algebra of Matrices

8.5 Inverses of Matrices

• Examples
• Example 1: Matrix Equation
• Example 2: Finding the Inverse of a Matrix
• Example 3: Finding the Inverse of a Matrix
• Example 4: Inverse Matrix Method
• Bonus Videos
• Bonus 1: Inverses of Matrices

8.6 Linear Programming

• Examples
• Example 1: Feasible Regions
• Example 2: Linear Programming
• Example 3: Linear Programming
• Example 4: Linear Programming
• Bonus Videos
• Bonus 1: Linear Programming

8.7 Nonlinear Systems of Equations

• Examples
• Example 1: Solving Nonlinear Systems by Graphing
• Example 2: Solving Nonlinear Systems by Graphing
• Example 3: Solving Nonlinear Systems Algebraically
• Example 4: Solving Nonlinear Systems Algebraically
• Example 5: Solving Nonlinear Systems Algebraically
• Bonus Videos
• Bonus 1: Nonlinear Systems of Equations

9.1 Sequences and Series

• Examples
• Example 1: Sequences
• Example 2: Recursively Defined Sequences
• Example 3: Finding the Formula for a Sequence
• Example 4: Evaluating Sums
• Example 5: Evaluating Sums
• Example 6: Evaluating Partial Sums and Series
• Bonus Videos
• Bonus 1: Sequences and Series

9.2 Arithmetic Sequences and Series

• Examples
• Example 1: General Term of an Arithmetic Sequence
• Example 2: Modeling Population Growth
• Example 3: Partial Sums of Arithmetic Sequences
• Example 4: Partial Sums of Arithmetic Sequences
• Bonus Videos
• Bonus 1: Arithmetic Sequences and Series

9.3 Geometric Sequences and Series

• Examples
• Example 1: General Term of a Geometric Sequence
• Example 2: General Term of a Geometric Sequence
• Example 3: Comparing Salary Offers
• Example 4: Partial Sum of a Geometric Sequence
• Example 5: Infinite Geometric Series
• Bonus Videos
• Bonus 1: Geometric Sequences and Series

9.4 Mathematical Induction

• Examples
• Example 1: Proof by Mathematical Induction
• Example 2: Proof by Mathematical Induction
• Example 3: Proof by Mathematical Induction
• Example 4: Proof by Mathematical Induction
• Bonus Videos
• Bonus 1: Mathematical Induction

9.5a An Introduction to Combinatorics - Counting, Permutations, and Combinations

• Examples
• Example 1: Counting Phone Numbers
• Example 2: The Multiplication Principle of Counting
• Example 3: Permutations
• Example 4: Permutations
• Example 5: Permutation Formula
• Example 6: Permutations and Combinations
• Example 7: Forming Committees
• Example 8: Forming "Words"
• Bonus Videos
• Bonus 1: An Introduction to Combinatorics - Counting, Permutations, and Combinations

9.5b An Introduction to Combinatorics - The Binomial and Multinomial Theorems

• Examples
• Example 1: Binomial Expansion
• Example 2: The Binomial Theorem
• Example 3: The Multinomial Theorem
• Bonus Videos
• Bonus 1: An Introduction to Combinatorics - The Binomial and Multinomial Theorems

9.6 An Introduction to Probability

• Examples
• Example 1: Probabilities when Outcomes are Equally Likely
• Example 2: Computing Probabilities
• Example 3: Computing Probabilities
• Example 4: Probability of a Union of Two Events
• Example 5: Unions of Mutually Exclusive Events
• Example 6: Independent Events
• Bonus Videos
• Bonus 1: An Introduction to Probability

A.1 Introduction to Polynomial Equations and Graphs (excluding complex numbers)

• Examples
• Example 2: Graphing Polynomial Functions
• Example 3: Solving Polynomial Inequalities Using a Graph
• Example 4: Solving Polynomial Inequalities: Sign-Test Method
• Bonus Videos
• Bonus 1: Introduction to Polynomial Equations and Graphs (excluding complex numbers)

A.2 Polynomial Division and the Division Algorithm (excluding complex numbers)

• Examples
• Example 1: Polynomial Long Division
• Example 2: Polynomial Long Division
• Example 3: Synthetic Division
• Example 4: Constructing Polynomials
• Bonus Videos
• Bonus 1: Polynomial Division and the Division Algorithm (excluding complex numbers)

A.3 Locating Real Zeros of Polynomials (excluding complex numbers)

• Bonus Videos
• Bonus 1: Locating Real Zeros of Polynomials (excluding complex numbers)

A.4 The Fundamental Theorem of Algebra (excluding complex numbers)

• Examples
• Example 1: Graphing Polynomial Functions

A.5 Mathematical Models

A.6 Properties of Functions

• Examples
• Example 1: Using Symmetry to Graph Relations
• Example 2: Determining Intervals of Monotonicity
• Example 3: Modeling the Water Level of a River