Preparation for College Mathematics, 2nd Edition

1.1 Introduction to Whole Numbers

• Examples
• Example 1: Understanding Place Value
• Example 2: Understanding Place Value
• Example 3: Reading and Writing Whole Numbers
• Example 5: Reading and Writing Whole Numbers
• Example 7: Application: Reading Tables

1.2 Addition and Subtraction with Whole Numbers

• Examples
• Example 1: Adding Whole Numbers
• Example 2: Adding Whole Numbers When Carrying is Required
• Example 3: Adding Whole Numbers Using Sums of 10
• Example 4: Adding Whole Numbers
• Example 5: Recognizing the Properties of Addition
• Example 7: Application: Calculating the Perimeter of a Rectangle
• Example 8: Subtracting Whole Numbers
• Example 9: Subtracting Whole Numbers
• Example 10: Subtracting Whole Numbers by Borrowing
• Example 11: Subtracting Whole Numbers by Borrowing
• Example 12: Finding a Missing Addend
• Example 13: Application: Subtracting Whole Numbers
• Example 14: Application: Adding and Subtracting Numbers

1.3 Multiplication with Whole Numbers

• Examples
• Example 1: Recognizing the Properties of Multiplication
• Example 3: Using the Distributive Property
• Example 4: Multiplying Whole Numbers
• Example 5: Multiplying Whole Numbers
• Example 6: Multiplying Whole Numbers
• Example 7: Multiplying Whole Numbers that End with $0$s
• Example 8: Application: Calculating the Area of a Rectangle

1.4 Division with Whole Numbers

• Examples
• Example 1: Understanding the Basic of Division
• Example 2: Understanding Division with 0
• Example 3: Dividing Whole Numbers
• Example 4: Dividing Whole Numbers
• Example 5: Dividing Whole Numbers
• Example 7: Using Division to Find Factors
• Example 8: Application: Dividing Whole Numbers

1.5 Rounding and Estimating with Whole Numbers

• Examples
• Example 1: Rounding Whole Numbers
• Example 2: Rounding Whole Numbers
• Example 3: Application: Rounding Whole Numbers
• Example 4: Estimating a Sum of Whole Numbers
• Example 6: Estimating a Difference of Whole Numbers
• Example 7: Application: Estimating a Difference of Whole Numbers
• Example 8: Estimating Products of Whole Numbers
• Example 9: Estimating Products of Whole Numbers
• Example 10: Estimating Quotients of Whole Numbers
• Example 11: Estimating Quotients of Whole Numbers
• Example 13: Estimating Quotients of Whole Numbers

1.6 Problem Solving with Whole Numbers

• Examples
• Example 1: Application: Adding Whole Numbers
• Example 2: Application: Multiplying Whole Numbers
• Example 3: Application: Dividing Whole Numbers
• Example 4: Application: Calculating Loan Amounts
• Example 5: Application: Balancing a Checking Account
• Example 6: Application: Finding the Area of Rectangles
• Example 7: Calculating an Average
• Example 8: Application: Calculating an Average
• Example 9: Application: Calculating an Average
• Example 10: Application: Calculating an Average

1.7 Solving Equations with Whole Numbers (x + b = c and ax = c)

• Examples
• Example 1: Checking Solutions to an Equation
• Example 2: Solving Equations of the form x + b = c
• Example 3: Solving Equations of the Form x + b = c
• Example 4: Solving Equations of the Form x + b = c
• Example 5: Solving Equations of the form ax = c
• Example 6: Solving Equations of the Form ax = c
• Example 7: Solving Equations of the Form ax = c

1.8 Exponents and Order of Operations

• 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: Using the Order of Operations with Whole Numbers
• Example 8: Using the Order of Operations with Whole Numbers
• Example 9: Using the Order of Operations with Whole Numbers

1.9 Tests for Divisibility

• Examples
• Example 1: Divisibility by 2
• Example 2: Divisibility by 3
• Example 3: Divisibility by 4
• Example 4: Divisibility by 5
• Example 5: Divisibility by 6
• Example 6: Divisibility by 9
• Example 7: Divisibility by 10

1.10 Prime Numbers and Prime Factorizations

• Examples
• Example 1: Determining Prime Numbers
• Example 2: Determining Composite Numbers
• Example 3: Determining Whether a Number is Prime
• Example 4: Determining Whether a Number is Prime
• Example 5: Determining Whether a Number is Prime
• Example 7: Finding the Prime Factorization of a Number
• Example 8: Finding the Prime Factorization of a Number
• Example 10: Finding the Factors of a Composite Number
• Example 12: Using Factors of Counting Numbers

2.1 Introduction to Integers

• Examples
• Example 1: Finding the Opposite of an Integer
• Example 2: Graphing Integers
• Example 3: Verifying Inequalities
• Example 4: Finding Absolute Value
• Example 5: Finding Absolute Value
• Example 6: Simplifying Expressions Containing Absolute Value
• Example 7: Verifying Absolute Value Inequalities
• Example 8: Solving Absolute Value Equations
• Example 9: Solving Absolute Values Equations

2.2 Addition with Integers

• Examples
• Example 1: Adding Integers
• Example 2: Adding Integers
• Example 3: Finding Additive Inverses
• Example 4: Checking Solutions in Equations

2.3 Subtraction with Integers

• Examples
• Example 1: Subtracting Integers
• Example 2: Subtracting Integers
• Example 3: Addition and Subtraction with Integers
• Example 4: Application: Calculating Change in Values
• Example 5: Application: Calculating Change in Value
• Example 6: Application: Calculating Net Change
• Example 7: Checking Solutions in Equations

2.4 Multiplication, Division, and Order of Operations with Integers

• Examples
• Example 1: Multiplying Integers
• Example 2: Multiplying Integers
• Example 3: Multiplying Integers
• Example 4: Dividing Integers
• Example 5: Division Involving 0
• Example 6: Using the Order of Operations with Integers
• Example 7: Using the Order of Operations with Integers
• Example 8: Using the Order of Operations with Integers
• Example 9: Using the Order of Operations with Integers
• Example 10: Order of Operations with Signed Integers
• Example 12: Application: Calculating an Average
• Example 13: Application: Calculating an Average

2.5 Simplifying and Evaluating Expressions

• Examples
• Example 1: Identifying Like Terms
• Example 2: Combining Like Terms
• Example 3: Evaluating Expressions
• Example 4: Simplifying and Evaluating Expressions
• Example 5: Simplifying and Evaluating Expressions

2.6 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

2.7 Solving Equations With Integers (ax + b = c)

• Examples
• Example 1: Verifying the Solution to an Equation
• Example 2: Solving Equations of the Form x + b = c
• Example 3: Solving Equations of the Form ax = c
• Example 4: Solving Equations of the form ax + b = c
• Example 5: Solving Equations of the Form ax + b = c
• Example 6: Solving Equations of the Form ax + b = c
• Example 7: Solving Equations of the form ax + b = c
• Example 9: Application: Solving Equations of the Form $ax+b=c$

3.1 Introduction to Fractions and Mixed Numbers

• Examples
• Example 1: Understanding Fractions
• Example 2: Understanding Fractions
• Example 3: Understanding Proper Fractions
• Example 4: Understanding Improper Fractions
• Example 5: Evaluating Fractions Involving 0
• Example 6: Placing Negative Signs in Fractions
• Example 7: Graphing Proper Fractions
• Example 8: Graphing Improper Fractions
• Example 9: Identifying Types of Fractions and Mixed Numbers
• Example 10: Application: Understanding Mixed Numbers
• Example 11: Application: Understanding Mixed Numbers
• Example 12: Graphing Mixed Numbers
• Example 13: Changing Mixed Numbers to Improper Fractions
• Example 14: Changing Mixed Numbers to Improper Fractions
• Example 15: Changing Improper Fractions to Mixed Numbers
• Example 16: Changing Improper Fractions to Mixed Numbers

3.2 Multiplication 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 7: Reducing Fractions to Lowest Terms
• Example 9: Application: Reducing Fractions to Lowest Terms
• Example 10: Multiplying and Reducing Using Prime Factors
• Example 11: Multiplying and Reducing Using Prime Factors
• Example 12: Multiplying and Reducing Using Prime Factors
• Example 15: Application: Multiplying and Reducing Fractions
• Example 16: Multiplying and Reducing Using the Division Method
• Example 17: Multiplying and Reducing Using the Division Method
• Example 18: Multiplying and Reducing Using the Division Method

3.3 Division with Fractions

• Examples
• Example 1: Finding Reciprocals
• Example 3: Dividing Fractions
• Example 4: Dividing Fractions
• Example 5: Dividing and Reducing Fractions
• Example 8: Finding a Missing Number
• Example 9: Application: Dividing Fractions
• Example 10: Application: Multiplying and Dividing Fractions

3.4 Multiplication and Division with Mixed Numbers

• Examples
• Example 1: Multiplying Mixed Numbers
• Example 2: Multiplying and Reducing Mixed Numbers
• Example 3: Multiplying and Reducing Mixed Numbers
• Example 4: Multiplying and Reducing Mixed Numbers
• Example 6: Finding Fractional Parts of Mixed Numbers
• Example 7: Finding Fractional Parts of Mixed Numbers
• Example 8: Application: Finding the Area of a Rectangle
• Example 9: Finding the Area of a Triangle
• Example 10: Dividing and Reducing Mixed Numbers
• Example 11: Dividing and Reducing Mixed Numbers
• Example 13: Application: Dividing Mixed Numbers

3.5 Least Common Multiple (LCM)

• Examples
• Example 1: Finding the Least Common Multiple (LCM)
• Example 2: Finding the Least Common Multiple (LCM)
• Example 4: Finding the Least Common Multiple (LCM)
• Example 5: Finding the Least Common Multiple (LCM)
• Example 6: Finding the Least Common Multiple (LCM)
• Example 7: Find the Least Common Multiple (LCM)
• Example 9: Application: Finding the LCM
• Example 10: Finding the LCM of a Set of Algebraic Terms
• Example 11: Finding the LCM of a Set of Algebraic Terms
• Example 13: Finding Equivalent Fractions
• Example 14: Finding Equivalent Fractions

3.6 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: Subtracting Fractions with the Same Denominator
• Example 8: Subtracting Fractions with Different Denominators
• Example 9: Subtracting Fractions with Different Denominators
• Example 10: Subtracting Fractions with Different Denominators
• Example 11: Application: Subtracting Fractions with Different Denominators
• Example 12: Adding and Subtracting Fractions Containing Variables
• Example 13: Adding Fractions Containing Variables
• Example 14: Adding Fractions Containing Variables
• Example 15: Subtracting Fractions Containing Variables

3.7 Addition and Subtraction with Mixed Numbers

• Examples
• Example 1: Adding Mixed Numbers with the Same Denominator
• Example 2: Adding Mixed Numbers with Different Denominators
• Example 3: Adding Mixed Numbers
• Example 4: Calculating Perimeter
• Example 5: Subtracting Mixed Numbers with the Same Denominator
• Example 6: Subtracting Mixed Numbers with Different Denominators
• Example 7: Subtracting Mixed Numbers with Borrowing
• Example 8: Subtracting Mixed Numbers with Borrowing
• Example 9: Subtracting Mixed Numbers by Borrowing
• Example 11: Application: Subtracting Mixed Numbers
• Example 12: Finding Sums of Negative Mixed Numbers
• Example 13: Finding Sums with Negative Mixed Numbers
• Example 14: Adding Mixed Numbers Using Improper Fractions
• Example 15: Adding Mixed Numbers Using Improper Fractions
• Example 16: Subtracting Mixed Numbers Using Improper Fractions

3.8 Comparisons and Order of Operations with Fractions

• Examples
• Example 1: Comparing Fractions
• Example 2: Comparing Fractions
• Example 3: Comparing Fractions
• Example 4: Using the Order of Operations with Fractions
• Example 5: Using the Order of Operations with Fractions
• Example 6: Using the Order of Operations with Fractions
• Example 8: Using the Order of Operations with Variables
• Example 9: Finding the Average
• Example 10: Simplifying Complex Fractions
• Example 11: Simplifying Complex Fractions
• Example 12: Simplifying Complex Fractions

3.9 Solving Equations with Fractions

• Examples
• Example 1: Solving Equations with Fractions
• Example 2: Solving Equations with Fractions
• Example 3: Solving Equations with Fractions
• Example 4: Solving Equations with Fractions
• Example 5: Solving Equations with Fractions
• Example 6: Solving Equations with Fractions

3.10 Ratios and Unit Rates

• Examples
• Example 1: Application: Writing Ratios
• Example 2: Writing Ratios that Compare Mixed Numbers
• Example 3: Writing Ratios that Compare Numbers
• Example 4: Application: Writing Ratios from Graphs
• Example 5: Writing Ratios in Geometry
• Example 6: Writing Ratios that Compare Measurements
• Example 7: Writing a Rate
• Example 10: Application: Writing a Unit Rate

3.11 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

3.12 Probability

• Examples
• Example 1: Finding All Outcomes Using a Tree Diagram
• Example 2: Finding the Sample Space Using a Tree Diagram
• Example 3: Finding the Sample Space Using a Tree Diagram
• Example 4: Calculating a Probability
• Example 5: Calculating a Probability
• Example 6: Calculating a Probability

4.1 Introduction to Decimal Numbers

• Examples
• Example 1: Reading and Writing Decimal Numbers
• Example 2: Reading and Writing Decimal Numbers
• Example 3: Reading and Writing Decimal Numbers
• Example 4: Comparing Positive Decimal Numbers
• Example 5: Comparing Positive Decimal Numbers
• Example 6: Comparing Negative Decimal Numbers
• Example 7: Rounding Decimal Numbers
• Example 8: Rounding Decimal Numbers

4.2 Addition and Subtraction with Decimal Numbers

• Examples
• Example 1: Adding Decimal Numbers
• Example 2: Adding Decimal Numbers
• Example 3: Adding Decimal Numbers
• Example 4: Application: Adding Decimal Numbers
• Example 5: Subtracting Decimal Numbers
• Example 6: Subtracting Decimal Numbers
• Example 7: Adding Signed Decimal Numbers
• Example 8: Subtracting Signed Decimal Numbers
• Example 9: Application: Adding and Subtracting Decimal Numbers
• Example 10: Combining Like Terms with Decimal Coefficients
• Example 11: Combining Like Terms with Decimal Coefficients

4.3 Multiplication and Division with Decimal Numbers

• Examples
• Example 1: Multiplying Decimal Numbers
• Example 2: Multiplying Decimal Numbers
• Example 3: Multiplying Decimal Numbers
• Example 5: Application: Multiplying Decimal Numbers
• Example 6: Multiplying by Powers of 10
• Example 7: Dividing Decimal Numbers
• Example 8: Dividing Positive and Negative Decimal Numbers
• Example 9: Dividing Decimal Numbers
• Example 10: Dividing Decimal Numbers
• Example 11: Application: Calculating Average Amount per Unit
• Example 12: Application: Calculating Total Distance Traveled
• Example 13: Dividing by Powers of 10

4.4 Estimating and Order of Operations with Decimal Numbers

• Examples
• Example 1: Estimating Sums of Decimal Numbers
• Example 3: Estimating Products of Decimal Numbers
• Example 4: Estimating Quotients of Decimal Numbers
• Example 5: Application: Estimating with Decimal Numbers
• Example 6: Using the Order of Operations with Decimal Numbers
• Example 7: Using the Order of Operations with Decimal Numbers
• Example 8: Using the Order of Operations with Decimal Numbers

4.5 Statistics: Mean, Median, Mode, and Range

• Examples
• Example 1: Application: Finding the Mean
• Example 2: Application: Finding the Median
• Example 3: Application: Finding the Mode and Range

4.6 Decimal Numbers and Fractions

• Examples
• Example 1: Changing Decimal Numbers to Fractions
• Example 3: Changing Decimal Numbers to Fractions
• Example 4: Changing Fractions to Decimal Numbers
• Example 5: Changing Fractions to Decimal Numbers
• Example 6: Changing Fractions to Decimal Numbers
• Example 7: Changing Fractions to Decimal Numbers
• Example 8: Simplifying Expressions with Decimals and Fractions
• Example 9: Comparing Decimals Numbers and Fractions
• Example 10: Simplifying Expressions with Decimals and Fractions
• Example 11: Evaluating Expressions with Decimals and Fractions
• Example 12: Application: Decimal and Fraction Expressions

4.7 Solving Equations with Decimal Numbers

• Examples
• Example 1: Solve Equations of the Form ax + b = c
• Example 2: Solve Equations of the Form ax + b = cx + d
• Example 3: Solve Equations of the Form ax + b = cx + d
• Example 4: Solve Equations of the Form ax + b = cx + d
• Example 6: Application: Solving Equations
• Example 7: Application: Solving Equations

5.1 Basics of Percent

• 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

5.2 Solving Percent Problems Using Proportions

• Examples
• Example 1: Finding the Amount
• Example 2: Finding the Base
• Example 3: Finding the Percent
• Example 4: Application: Finding the Amount
• Example 5: Application: Finding the Percent

5.3 Solving Percent Problems Using Equations

• Examples
• Example 1: Finding the Amount
• Example 2: Finding the Base
• Example 3: Finding the Percent
• Example 4: Finding the Amount
• Example 5: Finding the Base
• Example 6: Application: Finding the Base
• Example 7: Application: Finding the Amount

5.4 Applications of Percent

• Examples
• Example 1: Application: Solving Discount Problems
• Example 2: Application: Solving Discount Problems
• Example 3: Application: Solving Sales Tax Problems
• Example 4: Application: Solving Commission Problems
• Example 5: Finding the Percent Increase
• Example 6: Finding the Percent Decrease
• Example 7: Application: Calculating Percent of Profit

5.5 Simple and Compound Interest

• Examples
• Example 1: Application: Calculating Simple Interest
• Example 3: Application: Calculating Total Amount Due
• Example 4: Application: Calculating Principal using Simple Interest
• Example 5: Application: Calculating Time using Simple Interest
• Example 6: Application: Calculating Compound Interest
• Example 7: Application: Calculating Compound Interest
• Example 8: Application: Using the Compound Interest Formula
• Example 9: Application: Calculating Total Interest Earned
• Example 11: Application: Calculating Inflation
• Example 12: Application: Calculating the Current Value Due to Depreciation

5.6 Reading Graphs

• Examples
• Example 1: Reading a Bar Graph
• Example 2: Reading a Circle Graph
• Example 3: Reading a Line Graph
• Example 4: Reading a Histogram

6.1 US Measurements

• Examples
• Example 1: Basic Conversions in the US Customary System
• Example 2: Converting US Units of Measure Using Multiplication/Division
• Example 3: Application: Converting US Units of Measure
• Example 4: Using Unit Fractions to Convert US Units of Measure
• Example 5: Application: Converting US Units of Measure
• Example 6: Application: Converting US Units of Measure

6.2 The Metric System: Length and Area

• Examples
• Example 1: Converting Metric Units of Length
• Example 2: Application: Converting Metric Units of Length
• Example 3: Converting Metric Units of Length
• Example 4: Converting Metric Units of Length
• Example 5: The Prefixes Mega-, Giga-, and Tera-
• Example 6: Converting Metric Units of Area
• Example 7: Converting Metric Units of Area
• Example 8: Converting Metric Units of Area
• Example 9: Converting Metric Units of Land Area

6.3 The Metric System: Capacity and Weight

• Examples
• Example 1: Common Metric Units of Capacity
• Example 2: Converting Metric Units of Capacity
• Example 3: Converting Metric Units of Capacity
• Example 4: Converting Metric Units of Capacity
• Example 5: Application: Converting Metric Units of Capacity
• Example 7: Converting Metric Units of Weight
• Example 8: Application: Converting Metric Units of Weight

6.4 US and Metric Equivalents

• Examples
• Example 1: Equivalent Measures of Temperature
• Example 2: Converting Units of Temperature
• Example 3: Converting Units of Temperature
• Example 4: Converting Units of Length
• Example 5: Converting Units of Area
• Example 6: Converting Units of Capacity (Liquid Volume)
• Example 7: Converting Units of Weight (Mass)

6.5 Angles and Triangles

• Examples
• Example 1: Measuring Angles
• Example 2: Classifying Angles by Their Measure
• Example 3: Identifying Complementary and Supplementary Angles
• Example 4: Calculating Measures of Angles
• Example 5: Identifying Congruent Angles
• Example 6: Calculating Measures of Angles
• Example 7: Finding Adjacent Angles
• Example 8: Calculating Measures of Angles
• Example 9: Classifying a Triangle by Its Sides
• Example 10: Determining Whether a Triangle Exists
• Example 11: Analyzing Triangles

6.6 Perimeter

• Examples
• Example 1: Calculating the Perimeter of a Square
• Example 2: Calculating the Perimeter of a Triangle
• Example 3: Calculating the Perimeter of a Rectangle
• Example 4: Calculating the Perimeter of a Polygon
• Example 5: Calculating the Perimeter of a Polygon
• Example 6: Application: Calculating the Perimeter of a Polygon

6.7 Area

• Examples
• Example 1: Calculating the Area of a Triangle Using a Formula
• Example 2: Calculating the Area of a Trapezoid Using a Formula
• Example 3: Calculating the Area of a Circle
• Example 4: Calculating the Area of a Composite Figure
• Example 5: Calculating Area
• Example 6: Calculating Area
• Example 7: Calculating Area
• Example 8: Application: Calculating the Perimeter and Area

6.8 Volume and Surface Area

• Examples
• Example 1: Calculating the Volume of a Rectangular Solid
• Example 2: Calculating the Volume of a Sphere
• Example 3: Calculating the Volume of a Cone
• Example 4: Calculating the Volume of a Solid
• Example 5: Finding the Volume of a Cube
• Example 6: Calculating the Surface Area of a Rectangular Solid
• Example 7: Calculating the Surface Area of a Cylinder

6.9 Similar and Congruent Triangles

• Examples
• Example 1: Determining Whether Triangles are Similar
• Example 2: Finding Unknown Values Using Similar Triangles
• Example 3: Application: Finding Unknown Values Using Similar Triangles
• Example 4: Determining Whether Triangles are Congruent

6.10 Square Roots and the Pythagorean Theorem

• Examples
• Example 1: Evaluating Perfect Squares
• Example 2: Evaluating Square Roots
• Example 3: Evaluating Expressions Containing Square Roots
• Example 5: Verifying Right Triangles
• Example 6: Finding the Length of the Hypotenuse
• Example 7: Finding the Length of a Leg
• Example 8: Application: Finding the Length of the Hypotenuse

7.1 Properties of Real Numbers

• Examples
• Example 1: Identifying Properties of Addition and Multiplication
• Example 2: Identifying Properties of Addition and Multiplication

7.2 Solving Linear Equations: x + b = c and ax = c

• Examples
• Example 1: Checking Given Solutions in Equations
• Example 2: Solving Linear Equations of the Form x + b = c
• Example 3: Solving Linear Equations of the Form x + b = c
• Example 4: Solving Linear Equations of the Form x + b = c
• Example 5: Solving Linear Equations of the Form x + b = c
• Example 6: Simplifying and Solving Linear Equations
• Example 8: Solving Linear Equations of the Form ax = c
• Example 9: Solving Linear Equations of the Form ax=c
• Example 10: Solving Linear Equations of the Form ax = c
• Example 12: Application: Solving Linear Equations

7.3 Solving Linear Equations: ax + b = c

• Examples
• Example 1: Solving Linear Equations of the Form ax + b = c
• Example 2: Solving Linear Equations of the Form ax + b = c
• Example 3: Solving Linear Equations Involving Decimals
• Example 4: Solving Linear Equations Involving Decimals
• Example 5: Solving Linear Equations Involving Fractions
• Example 6: Solving Linear Equations Involving Fractions

7.4 Solving Linear Equations: ax + b = cx + d

• Examples
• Example 1: Solving Equations of the Form ax + b = cx + d
• Example 2: Solving Equations of the Form ax + b = cx + d
• Example 3: Solving Linear Equations Involving Decimals
• Example 4: Solving Linear Equations Involving Fractions
• Example 5: Solving Equations Involving Parentheses
• Example 6: Solving Equations Involving Parentheses
• Example 8: Determining Types of Equations
• Example 9: Determining Types of Equations
• Example 10: Determining Types of Equations

7.5 Working with Formulas

• Examples
• Example 1: Application: Evaluating Formulas
• Example 2: Evaluating Formulas
• Example 3: Application: Evaluating Formulas
• Example 4: Evaluating Formulas
• Example 5: Solving for Different Variables
• Example 6: Solving for Different Variables
• Example 7: Solving for Different Variables
• Example 8: Solving for Different Variables

7.6 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

7.7 Applications: Distance-Rate-Time, Interest, Average, and Cost

• Examples
• Example 1: Application: Solving Distance-Rate-Time Problems
• Example 2: Application: Solving Distance-Rate-Time Problems
• Example 3: Application: Solving Interest Problems
• Example 4: Application: Finding the Average (or Mean)
• Example 5: Application: Using Bar Graphs
• Example 6: Application: Calculating Cost

7.8 Solving Linear Inequalities

• Examples
• Example 1: Graphing Intervals
• Example 2: Graphing Intervals
• Example 3: Graphing Intervals
• Example 4: Graphing Intervals
• Example 5: Solving an Inequality and Graphing the Solution Set
• Example 6: Solving an Inequality and Graphing the Solution Set
• Example 7: Solving an Inequality and Graphing the Solution Set
• Example 8: Solving an Inequality and Graphing the Solution Set
• Example 9: Solving Linear Inequalities
• Example 10: Solving Linear Inequalities
• Example 11: Solving Linear Inequalities
• Example 13: Application: Using Inequalities

7.9 Compound Inequalities

• Examples
• Example 1: Finding the Union and Intersection of Two Sets
• Example 2: Finding the Union and Intersection of Two Sets
• Example 3: Finding the Union and Intersection of Two Sets
• Example 4: Graphing Compound Inequalities
• Example 5: Graphing Compound Inequalities
• Example 6: Solving Compound Inequalities Containing AND
• Example 7: Solving Compound Inequalities Containing AND
• Example 8: Solving Compound Inequalities Containing AND
• Example 9: Solving Compound Inequalities Containing OR
• Example 10: Solving Compound Inequalities Containing OR

7.10 Absolute Value Equations

• Examples
• Example 1: Solving Absolute Value Equations
• Example 2: Solving Equations with Two Absolute Value Expressions

7.11 Absolute Value Inequalities

• Examples
• Example 1: Solving Absolute Value Inequalities
• Example 2: Solving Absolute Value Inequalities
• Example 3: Solving Absolute Value Inequalities
• Example 4: Solving Absolute Value Inequalities
• Example 5: Solving Absolute Value Inequalities
• Example 6: Solving Absolute Value Inequalities
• Example 7: Solving Absolute Value Inequalities
• Example 8: Solving Absolute Value Inequalities
• Example 9: Solving Absolute Value Inequalities

8.1 The Cartesian Coordinate System

• Examples
• Example 1: Plotting Ordered Pairs
• Example 2: Plotting Ordered Pairs
• Example 3: Finding Ordered Pairs
• Example 4: Finding Ordered Pairs
• Example 6: Locating Points on the Graph of a Line

8.2 Graphing Linear Equations in Two Variables

• Examples
• Example 1: Graphing a Linear Equation in Two Variables
• Example 2: Graphing a Linear Equation in Two Variables
• Example 3: Graphing a Linear Equation in Two Variables
• Example 4: Using Intercepts to Graph Linear Equations
• Example 5: Using Intercepts to Graph Linear Equations
• Example 7: Graphing Horizontal Lines
• Example 8: Graphing Vertical Lines

8.3 Slope-Intercept Form

• Examples
• Example 1: Finding the Slope of a Line
• Example 2: Finding the Slope of a Line
• Example 3: Finding the Slope of a Horizontal Line
• Example 4: Finding the Slope of a Vertical Line
• Example 5: Using Slope and the y‑Intercept to Graph a Line
• Example 6: Using Slope and the y-Intercept to Graph a Line
• Example 7: Finding Equations Given the Slope and the y‑Intercept

8.4 Point-Slope Form

• Examples
• Example 1: Graphing a Line Given a Point and the Slope
• Example 2: Finding Equations of Lines Using the Slope and a Point
• Example 3: Finding Equations of Lines Using Two Points
• Example 4: Finding Equations of Lines Using a Graph
• Example 5: Finding the Equations of Parallel Lines
• Example 6: Finding the Equations of Perpendicular Lines

8.5 Introduction to Functions and Function Notation

• Examples
• Example 1: Finding the Domain and Range
• Example 2: Reading the Domain and Range from the Graph of a Relation
• Example 3: Determining if a Relation is a Function
• Example 4: Using the Vertical Line Test
• Example 5: Finding the Domain of a Function
• Example 6: Evaluating Functions
• Example 7: Evaluating Nonlinear Functions
• Example 8: Evaluating Functions From a Graph

8.6 Graphing Linear Inequalities in Two Variables

• Examples
• Example 1: Graphing Linear Inequalities
• Example 2: Graphing Linear Inequalities
• Example 3: Graphing Linear Inequalities
• Example 4: Graphing Linear Inequalities

9.1 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

9.2 Systems of Linear Equations: Solutions by Substitution

• Examples
• Example 1: Solving Systems by Substitution (One Solution)
• Example 2: Solving Systems by Substitution (One Solution)
• Example 3: Solving Systems by Substitution (No Solution)
• Example 4: Solving Systems by Substitution (Infinite Solutions)
• Example 5: Solving Systems by Substitution (Decimal Numbers)

9.3 Systems of Linear Equations: Solutions by Addition

• Examples
• Example 1: Solving Systems by Addition (One Solution)
• Example 2: Solving Systems by Addition (Infinite Solutions)
• Example 3: Solving Systems by Addition (No Solution)
• Example 4: Solving Systems by Addition (Decimal Numbers)
• Example 6: Using a System to Find the Equation of a Line

9.4 Applications: Distance-Rate-Time, Number Problems, Amounts, and Costs

• Examples
• Example 1: Application: Distance-Rate-Time (Rates Unknown)
• Example 2: Application: Distance-Rate-Time (Times Unknown)
• Example 3: Solving a Number Problem
• Example 4: Application: Counting Coins
• Example 5: Application: Calculating Age
• Example 6: Application: Finding Amounts and Costs

9.5 Applications: Interest and Mixture

• Examples
• Example 1: Application: Calculating Interest and Balances
• Example 2: Application: Calculating Interest and Investments
• Example 3: Application: Solving a Mixture Problem
• Example 4: Application: Solving a Mixture Problem

9.6 Systems of Linear Equations: Three Variables

• Examples
• Example 1: Solving a System with Three Variables (One Solution)
• Example 2: Solving a System with Three Variables (No Solution)
• Example 3: Three Variables (A System with Infinitely Many Solutions)
• Example 4: Application: Using a System with Three Variables

9.7 Matrices and Gaussian Elimination

• Examples
• Example 1: Creating Coefficient and Augmented Matrices
• Example 2: Creating Coefficient and Augmented Matrices
• Example 3: Using Gaussian Elimination (Two Variables)
• Example 4: Using Gaussian Elimination (Three Variables)

9.8 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

10.1 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

10.2 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

10.3 Applications: Scientific Notation

• Examples
• Example 1: Writing Decimals in Scientific Notation
• Example 2: Using Scientific Notation while Simplifying
• Example 3: Application: Scientific Notation

10.4 Introduction to Polynomials

• Examples
• Example 1: Simplifying Polynomials
• Example 3: Evaluating Polynomials
• Example 4: Evaluating Polynomials
• Example 6: Evaluating Polynomials

10.5 Addition and Subtraction with Polynomials

• Examples
• Example 1: Adding Polynomials
• Example 2: Adding Polynomials
• Example 4: Subtracting Polynomials
• Example 5: Subtracting Polynomials
• Example 7: Simplifying Algebraic Expressions
• Example 8: Simplifying Algebraic Expressions

10.6 Multiplication with Polynomials

• Examples
• Example 1: Multiplying Polynomials and Monomials
• Example 3: Multiplying Two Binomials
• Example 5: Multiplying Polynomials
• Example 6: Multiplying Polynomials
• Example 7: Multiplying Polynomials
• Example 8: Multiplying Polynomials
• Example 9: Using the FOIL Method to Multiply Binomials
• Example 10: Using the FOIL Method to Multiply Binomials

10.7 Special Products of Binomials

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

10.8 Division with Polynomials

• Examples
• Example 1: Dividing by a Monomial
• Example 2: Using the Division Algorithm
• Example 3: Using Long Division (Remainder 0)
• Example 4: Using Long Division (Terms Missing)

10.9 Synthetic Division and the Remainder Theorem

• Examples
• Example 1: Using Synthetic Division
• Example 2: Using the Remainder Theorem and Synthetic Division
• Example 3: Using the Remainder Theorem and Synthetic Division
• Example 4: Using the Remainder Theorem and Synthetic Division

11.1 Greatest Common Factor (GCF) and Factoring by Grouping

• Examples
• Example 1: Finding the GCF
• Example 2: Factoring Out the GCF of a Polynomial
• Example 3: Factoring Out the GCF of a Polynomial
• Example 4: Factoring Out the GCF of a Polynomial
• Example 5: Factoring Out the GCF of a Multi-Variable Polynomial
• Example 6: Factoring Out a Common Binomial Factor
• Example 7: Factoring Polynomials by Grouping
• Example 8: Factoring Polynomials by Grouping
• Example 9: Factoring Polynomials by Grouping
• Example 10: Factoring Polynomials by Grouping
• Example 11: Factoring Polynomials by Grouping

11.2 Factoring Trinomials: x^2+bx+c

• Examples
• Example 1: Factoring Trinomials with Leading Coefficient 1
• Example 2: Factoring Trinomials with Leading Coefficients of 1
• Example 4: Finding a Common Monomial Factor

11.3 Factoring Trinomials: ax^2+bx+c

• Examples
• Example 1: Using the Trial-and-Error Method
• Example 2: Factoring Trinomials
• Example 3: Using the ac-Method
• Example 4: Using the ac-Method
• Example 5: Using the ac-Method

11.4 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
• Example 4: Factoring Sums and Differences of Two Cubes

11.5 Review of Factoring Techniques

11.6 Solving Quadratic Equations by Factoring

• Examples
• Example 1: Solving Factored Quadratic Equations
• Example 2: Solving Quadratic Equations by Factoring
• Example 3: Solving Quadratic Equations by Factoring
• Example 4: Solving Quadratic Equations by Factoring
• Example 5: Solving Quadratic Equations by Factoring
• Example 6: Solving Quadratic Equations by Factoring
• Example 7: Solving Quadratic Equations by Factoring
• Example 9: Solving Higher Degree Equations
• Example 10: Finding Equations with Given Roots

11.7 Applications: Quadratic Equations

• Examples
• Example 1: Solving Quadratic Number Problems
• Example 2: Application: Solving Quadratic Equations
• Example 3: Application: Solving Quadratic Number Problems
• Example 4: Application: Solving Quadratic Equations
• Example 5: Consecutive Integers
• Example 6: Consecutive Integers
• Example 7: Application: The Pythagorean Theorem

12.1 Introduction to Rational Expressions

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

12.2 Multiplication and Division with Rational Expressions

• Examples
• Example 1: Multiplication with Rational Expressions
• Example 2: Multiplying with Rational Expressions
• Example 3: Multiplying with Rational Expressions
• Example 4: Multiplying with Rational Expressions
• Example 6: Dividing with Rational Expressions
• Example 7: Dividing with Rational Expressions
• Example 8: Dividing with Rational Expressions

12.3 Least Common Multiple of Polynomials

• Examples
• Example 1: Finding the LCM of a Set of Counting Numbers
• Example 2: Adding Fractions with the Same Denominator
• Example 3: Adding Fractions with Different Denominators
• Example 4: Finding the LCM of Polynomials
• Example 5: Finding the LCM of Polynomials
• Example 6: Writing Equivalent Rational Expressions
• Example 7: Writing Equivalent Rational Expressions

12.4 Addition and Subtraction with Rational Expressions

• Examples
• Example 1: Adding Rational Expressions with a Common Denominator
• Example 2: Adding Rational Expressions with Different Denominators
• Example 4: Subtracting Rational Expressions with a Common Denominator
• Example 5: Subtracting Rational Expressions with Different Denominators
• Example 7: Adding and Subtracting Rational Expressions

12.5 Simplifying Complex Fractions

• Examples
• Example 1: First Method for Simplifying Complex Fractions
• Example 2: First Method for Simplifying Complex Fractions
• Example 3: First Method for Simplifying Complex Fractions
• Example 4: Second Method for Simplifying Complex Fractions
• Example 5: Second Method for Simplifying Complex Fractions
• Example 6: Simplifying Complex Algebraic Expressions

12.6 Solving Rational Equations

• Examples
• Example 1: Proportions
• Example 2: Application of Proportions
• Example 3: Solving Rational Equations
• Example 4: Solving Rational Equations
• Example 5: Solving Rational Equations
• Example 7: Solving a Formula for a Specified Variable
• Example 8: Similar Triangles

12.7 Applications: Rational Expressions

• Examples
• Example 1: Fractions
• Example 2: Work Problems
• Example 3: Work Problems
• Example 4: Work Problems
• Example 5: Distance-Rate-Time
• Example 6: Distance-Rate-Time

12.8 Applications: Variation

• Examples
• Example 1: Direct Variation
• Example 2: Direct Variation
• Example 3: Inverse Variation
• Example 4: Inverse Variation
• Example 5: Joint Variation
• Example 6: More Variation
• Example 7: More Variation
• Example 8: More Variation

13.1 Evaluating Radicals

• Examples
• Example 1: Evaluating Square Roots
• Example 2: Evaluating Square Roots
• Example 3: Estimating Square Roots
• Example 4: Evaluating Cube Roots

13.2 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

13.3 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

13.4 Addition, Subtraction, and Multiplication with Radicals

• Examples
• Example 1: Adding and Subtracting with Radicals
• Example 3: Multiplying with Radicals

13.5 Rationalizing Denominators

• Examples
• Example 1: Rationalizing Denominators Containing Square Roots
• Example 2: Rationalizing Denominators Containing Cube Roots
• Example 3: Rationalizing Denominators

13.6 Solving Radical Equations

• Examples
• Example 1: Solving Equations with One Radical
• Example 2: Solving Equations with One Radical
• Example 3: Solving Equations with One Radical
• Example 4: Solving Equations with One Radical
• Example 6: Solving Equations with Two Radicals
• Example 7: Solving Equations with Two Radicals
• Example 8: Solving Equations containing a Cube Root

13.7 Functions with Radicals

• Examples
• Example 1: Finding the Domain of a Radical Function
• Example 2: Evaluating Radical Functions
• Example 3: Graphing a Radical Function

13.8 Introduction to Complex Numbers

• Examples
• Example 1: Finding the Square Roots of Negative Numbers
• Example 2: Identifying Real and Imaginary Parts
• Example 3: Solving Equations
• Example 4: Adding and Subtracting with Complex Numbers

13.9 Multiplication and Division with Complex Numbers

• Examples
• Example 1: Multiplying with Complex Numbers
• Example 2: Dividing with Complex Numbers
• Example 3: Simplifying Powers of i

14.1 Quadratic Equations: The Square Root Method

• Examples
• Example 1: Solving Quadratic Equations by Factoring
• Example 2: Solving Quadratic Equations by Factoring
• Example 3: Quadratic Equations Involving the Sum of Two Squares
• Example 4: Using the Square Root Property
• Example 5: Using the Square Root Property
• Example 7: The Pythagorean Theorem
• Example 8: The Pythagorean Theorem

14.2 Quadratic Equations: Completing the Square

• Examples
• Example 1: Completing the Square
• Example 2: Solving Quadratic Equations by Completing the Square
• Example 3: Solving Quadratic Equations by Completing the Square
• Example 4: Solving Quadratic Equations by Completing the Square
• Example 5: Solving Quadratic Equations by Completing the Square
• Example 7: Quadratic Equations with Known Roots
• Example 8: Quadratic Equations with Known Roots
• Example 9: Quadratic Equations with Known Roots

14.3 Quadratic Equations: The Quadratic Formula

• Examples
• Example 1: The Quadratic Formula
• Example 2: The Quadratic Formula
• Example 3: The Quadratic Formula
• Example 4: The Quadratic Formula
• Example 5: Cubic Equations
• Example 6: Finding the Discriminant
• Example 7: Understanding the Discriminant
• Example 8: Understanding the Discriminant

14.4 More Applications of Quadratic Equations

• Examples
• Example 1: Using The Pythagorean Theorem
• Example 2: Application: Work
• Example 3: Application: Distance-Rate-Time
• Example 4: Application: Projectiles
• Example 5: Finding the Dimensions of a Box
• Example 6: Finding the Dimensions of a Baseball Field
• Example 7: Application: Finding the Cost per Person

14.5 Equations in Quadratic Form

• Examples
• Example 1: Using Substitution to Solve Equations in Quadratic Form
• Example 2: Using Substitution to Solve Equations in Quadratic Form
• Example 3: Using Substitution to Solve Equations in Quadratic Form
• Example 4: Using Substitution to Solve Equations in Quadratic Form
• Example 5: Solving Rational Equations that Simplify to Quadratic Equations
• Example 6: Solving Higher-Degree Equations
• Example 7: Solving Higher-Degree Equations

14.6 Graphing Quadratic Functions

• Examples
• Example 1: Graphing Quadratic Functions
• Example 2: Graphing Quadratic Functions
• Example 3: Quadratic Functions
• Example 4: Graphing Quadratic Functions

14.7 More on Graphing Functions and Applications

• Examples
• Example 1: Graphing Quadratic Functions of the Form y = ax² + bx + c
• Example 2: Graphing Quadratic Functions of the Form y = ax² + bx + c
• Example 3: Graphing Quadratic Functions of the Form y = ax² + bx + c
• Example 4: Graphing Quadratic Functions of the Form y = ax² + bx + c
• Example 5: Application: Minimum and Maximum Values
• Example 6: Application: Minimum and Maximum Values

14.8 Solving Polynomial and Rational Inequalities

• Examples
• Example 1: Solving Polynomial Inequalities by Factoring
• Example 2: Solving Polynomial Inequalities by Factoring
• Example 3: Solving Polynomial Inequalities by Factoring
• Example 4: Solving Polynomial Inequalities Using the Quadratic Formula
• Example 5: Solving Polynomial Inequalities Using the Quadratic Formula
• Example 6: Solving Rational Inequalities
• Example 7: Solving Rational Inequalities
• Example 8: Solving Rational Inequalities

15.1 Algebra of Functions

• Examples
• Example 1: Algebraic Operations with Functions
• Example 2: Algebraic Operations with Functions
• Example 3: Algebraic Operations with Functions with Limited Domains
• Example 4: Algebraic Operations with Functions

15.2 Composition of Functions and Inverse Functions

• Examples
• Example 1: Evaluating a Function at an Algebraic Expression
• Example 2: Compositions
• Example 3: Compositions
• Example 4: Compositions
• Example 5: One-to-One Functions
• Example 6: Inverse Functions
• Example 7: Inverse Functions
• Example 8: Evaluating Compositions of Inverses
• Example 9: Finding the Inverse
• Example 10: Finding the Inverse

15.3 Exponential Functions

• Examples
• Example 1: Application: Calculating Bacterial Growth
• Example 2: Application: Calculating Bacterial Growth
• Example 3: Application: Calculating Compound Interest
• Example 4: Application: Calculating Compound Interest
• Example 5: Application: Calculating Compound Interest

15.4 Logarithmic Functions

• Examples
• Example 1: Translating Between Exponential and Logarithmic Form
• Example 2: Evaluating Logarithms
• Example 3: Solving Logarithmic Equations
• Example 4: Solving Logarithmic Equations

15.5 Properties of Logarithms

• Examples
• Example 1: Using the Product Rule of Logarithms
• Example 2: Using the Quotient Rule of Logarithms
• Example 3: Using the Power Rule
• Example 4: Using the Properties of Logarithms to Expand Expressions
• Example 5: Using the Properties of Logarithms to Write Expanded Forms as Single Logarithms

15.6 Common Logarithms and Natural Logarithms

• Examples
• Example 1: Translations Between Exponential Form and Common Logarithms
• Example 4: Translations between Exponential Form and Natural Logarithms

15.7 Logarithmic and Exponential Equations and Change-of-Base

• Examples
• Example 1: Solving Exponential Equations with the Same Base
• Example 2: Solving Exponential Equations with Different Bases
• Example 3: Solving Logarithmic Equations
• Example 4: Change-of-Base
• Example 5: Change-of-Base

15.8 Applications: Exponential and Logarithmic Functions

• Examples
• Example 1: Application: Exponential Growth
• Example 2: Application: Continuously Compounded Interest
• Example 3: Application: The Richter Scale
• Example 4: Application: The Richter Scale
• Example 5: Application: Half-life of Radium
• Example 6: Application: Newton's Law of Cooling

16.1 Translations and Reflections

• Examples
• Example 1: Using $f\left(x\right)$ Notation
• Example 2: Finding the Difference Quotient ${\displaystyle \frac{f\left(x+h\right)-f\left(x\right)}{h}}$
• Example 3: Finding the Difference Quotient $f\left(x+h\right)-{\displaystyle \frac{f\left(x\right)}{h}}$
• Example 4: Horizontal and Vertical Translations of y = |x|
• Example 5: Horizontal and Vertical Translations of y = |x|
• Example 6: Horizontal and Vertical Translations of y = |x|
• Example 7: Reflections and Translations of y = |x|
• Example 8: Graphing Translations of a Function Given its Graph
• Example 9: Graphing Translations of a Function Given Its Graph

16.2 Parabolas as Conic Sections

• Examples
• Example 1: Sketching Horizontal Parabolas
• Example 2: Sketching Horizontal Parabolas

16.3 Distance Formula, Midpoint Formula, and Circles

• Examples
• Example 1: Using the Distance Formula
• Example 2: Determining If a Triangle is a Right Triangle
• Example 3: Finding the Midpoint
• Example 4: Finding the Equation of a Circle
• Example 5: Finding the Equation of a Circle
• Example 6: Graphing a Circle

16.4 Ellipses and Hyperbolas

• Examples
• Example 1: Equation of an Ellipse—Major Axis Horizontal
• Example 2: Equation of an Ellipse—Major Axis Vertical
• Example 3: Hyperbola Opening Left and Right
• Example 4: Hyperbola Opening Up and Down
• Example 5: Ellipse with Center at $\left(h,k\right)$
• Example 6: Hyperbola with Center at (h, k)

16.5 Nonlinear Systems of Equations

• Examples
• Example 1: Solving a System of One Quadratic and One Linear Equation
• Example 2: Solving a System of One Quadratic and One Linear Equation
• Example 3: A System of Two Quadratic Equations