Algebra

1. Definitions: Relation, Function, Domain, Range

2. Introduction to Function Notation

3. Function Notation with an Equation

4. Interval Notation

5. Functions in Basic Applications

6. A Function Application with a Graph

7. Function Language: Independent and Dependent Variable

Constant Graphs

1. Graphing a Constant Function on a Restricted Domain 

Linear Graphs

1. The Solutions and the Graph of  a Linear Equation in Two Variables

2. Graphing Lines Using Two Points

3. Intercepts of Linear Equations in Two Variables

4. Graphing Lines Using Intercepts

5. The Slope of a Line

6. General Slopes Positive, Negative, Zero, and Undefined 

7. Graphing Linear Inequalities in Two Dimensions

Quadratic Graphs

1. Finding x- and y-intercepts of a Quadratic Function that Does Not Factor

2. Graphing a Quadratic Function in Standard Form By Using Symmetric Points

3. Examples of Graphing Quadratic Functions in Standard Form

4. Finding the Vertex of a Quadratic Function in Standard Form and then Determining if it is a Minimum or Maximum

5. Completing the Square to Write a Quadratic Function in Standard Form

6. The Vertex Formula for a Quadratic Function

7. An Application of the Vertex of a Quadratic Function 

Piecewise-Defined Graphs

1. Graphing a Piecewise-Defined Function

Circle Graphs

1. Pythagorean Theorem

2. Calculating the Distance Between Two Points (Ordered Pairs)

3. Finding One Coordinate of a Point Given the Distance Between that Point and Another Point

4. Graphing and Finding the Center and Radius of a Circle Given its Equation in Standard Form

5. Completing the Square to Write the Equation of a Circle in Standard Form

Transformations: Absolute Value, Power, Root, Exponential, and Logarithmic Functions

1. Common Parent Functions

2. Transformations of Functions

3. Identifying the Parent Function and Transformations

4. Graphing with Transformations Examples

5. Writing the Equation of a Transformed Function

6. Graphing Transformed Exponential Functions

7. Graphing Transformed Log Functions

8. Guided Practice: Using Transformations to Graph a Logarithmic Function

Polynomial Graphs

1. Defining End Behavior

2. Examples: End Behavior of a Polynomial Function

3. Guided Practice: Determining the Leading Term and End Behavior of Polynomial Functions

4. Determining Zeros and Multiplicities of Polynomials that Factor

5. Determining What Values Make a Polynomial Zero, Positive, or Negative

6. Using End Behavior, Zeros, and Multiplicities to Determine Intervals Where a Polynomial is Positive or Negative

7. Guided Practice: Using End Behavior, Zeros, and Multiplicities to Make a Sign Chart for a Polynomial Function

8. Examples: Graphing Factored Polynomial Functions Using Zeros and End Behavior

9. Examples: Graphing Polynomial Functions that are not Factored

10. Guided Practice: Graphing a Polynomial Function Using its Number Line Chart

Rational Function Graphs

1. Determining Values that make a Rational Function Zero, Undefined, Positive, and Negative

2. Defining End Behavior

3. Examples: End Behavior of a Rational Function

4. Guided Practice: Determining the End Behavior of a Rational Function

5. End Behaviors of Polynomial & Rational Functions

6. Sketching a Rational Function Graph

7. Sketching a Rational Function Graph with a Hole

8. Sketching a Rational Function Graph with a Horizontal Asymptote

9. Rational Functions with Oblique Asymptotes

Conic Section Graphs

1. The Parts of a Parabola and How They Relate

2. Geometric Property of a Parabola

3. Example: Finding and Graphing Parts of a Parabola

4. Introducing the Standard Equation of a Parabola with Examples

5. Example: Determining the Equation of a Parabola

6. The Parts of an Ellipse and How They Relate

7. The Geometric Property of an Ellipse

8. Example: Finding and Graphing the Parts of an Ellipse

9. Introducing the Standard Equation of an Ellipse with an Example

10. Example: Determining the Equation of an Ellipse

11. The Parts of a Hyperbola and How They Relate

12. Example: Finding and Graphing the Parts of an Hyperbola

13. Introducing the Standard Equation of a Hyperbola with an Example

14. Example: Determining the Equation of a Hyperbola

Graphing Inverses

1. Graphing an Inverse Function Using the Original Function Graph 

1. The Solutions and the Graph of  a Linear Equation in Two Variables

2. Graphing Lines Using Two Points

3. Intercepts of Linear Equations in Two Variables

4. Graphing Lines Using Intercepts

5. The Slope of a Line

6. General Slopes Positive, Negative, Zero, and Undefined 

7. The Slopes of Parallel Lines and Perpendicular Lines

8. Interpreting Slope and Rate of Change in Applications 

9. The Slope-Intercept Form of a Linear Equation in Two Variables

10. Examples Using the Slope-Intercept Form

11. Examples Determining the Slope-Intercept Equation of a Line

12. Point-Slope Form of a Linear Equation in Two Variables

13. A Function Application with a Graph

14. Creating a Linear Function Model to Make a Prediction 

15. Graphing a Linear Function on a Restricted Domain 

Quadratic Equations

1. Solving Quadratic and Other Polynomial Equations by Factoring

2. Factoring a Polynomial Versus Solving a Polynomial Equation 

3. Application of Quadratic Equations: Area of a Triangle

4. Application of Quadratic Equations: Gravity Problems

5. Application of Quadratic Equations: Right Triangles and the Pythagorean Theorem 

6. General Method of Completing the Square

7. Solving a Quadratic Equation by Using a Square Root (Completing the Square)

8. A Formula for Solving Quadratic Equations (The Quadratic Formula)

9. Solving a Quadratic Equation Using the Quadratic Formula 

Quadratic Functions

1. Graphing a Quadratic Function in Standard Form By Using Symmetric Points

2. Examples of Graphing Quadratic Functions in Standard Form

3. Finding the Vertex of a Quadratic Function in Standard Form and then Determining if it is a Minimum or Maximum

4. Completing the Square to Write a Quadratic Function in Standard Form

5. The Vertex Formula for a Quadratic Function

6. An Application of the Vertex of a Quadratic Function 

Two-Dimensional Systems of Linear Equations

1. Using Substitution to Solve 2D Systems of Equations with One Solution

2. Using Elimination to Solve 2D Systems of Equations with One Solution

3. Solving More Difficult Systems of Two-Dimensional Equations by Elimination

4. Systems Application: Cost, Revenue, and Profit

Three-Dimensional Systems of Linear Equations

1. Systems of Three Linear Equations

2. Determining a Quadratic Function from Three Points

Using an Augmented Matrix to Solve a System of Linear Equations

1. Solving a System of Three Linear Equations Using Its Augmented Matrix and Gaussian Elimination

2. Solving a System of Three Equations Using its Augmented Matrix (Gauss-Jordan)

3. Guided Practice: Solving a System of Three Equations Using its Augmented Matrix (Gauss-Jordan)

Systems of Linear Inequalities

1. Graphing Linear Inequalities in Two Dimensions

2. Solving Systems of Linear Inequalities in Two Dimensions

3. Guided Practice: Solving Systems of Linear Inequalities in Two Dimensions

Linear Programming

1. Maximizing or Minimizing an Objective Function Within Limitations

2. Guided Practice: Maximizing or Minimizing an Objective Function with Limitations

3. Linear Programming Example - Soybeans and Wheat

4. Linear Programming Example - Gear Manufacturing

1. Function Language: Independent and Dependent Variable

2. Functions in Basic Applications

3. A Function Application with a Graph

4. Creating a Linear Function Model to Make a Prediction

5. Interpreting Slope and Rate of Change in Applications 

6. Systems Application: Cost, Revenue, and Profit

7. Linear Programming

8. An Application of the Vertex of a Quadratic Function 

9. Application of Quadratic Equations: Area of a Triangle

10. Application of Quadratic Equations: Gravity Problems

11. Application of Quadratic Equations: Right Triangles and the Pythagorean Theorem 

12. Exponential Growth and Decay Models

13. Example: Exponential Growth Problem

14. Example: Exponential Decay Problem

15. Exponential Decay Example with Carbon-14

1. Determining f(x+h)

2. Difference Quotient

3. Difference Quotient for Rational Functions

4. Guided Practice: Determining the Difference Quotient for a Cubic Function

Basic Domain and Range

1. Definitions: Relation, Function, Domain, Range

2. Interval Notation 

3. Domain and Range of a Graph

4. Domain from a Function Equation

Domain of an Arithmetic Combination of Functions

1. Formulas and Domain for Adding, Subtracting, Multiplying and Dividing Functions 

2. Examples: Combining Functions with Arithmetic and Determining Domain

3. Guided Practice: Finding the Domain of the Quotient of Two Functions

4. Domain of Graphed Functions Combined with Arithmetic 

Domain of a Composition of Functions

1. Determining the Domain of a Composition of Functions 

2. Examples: Determining the Composition of Two Functions and its Domain

3. Guided Practice: Determine the Composition and Domain of a Square Root Function with a Rational Function

Domain of a Logarithmic Function

1. Domain of a Log Function

1. Intervals Where a Graph is Increasing, Decreasing, or Constant

2. Local (or Relative) Extrema of a Continuous Function

3. Guided Practice: Determining Local (Relative) Extrema and Where a Graph is Increasing, Decreasing, or Constant

1. What are Intercepts?

2. Intercepts of Linear Equations in Two Variables 

3. Graphing Lines Using Intercepts

4. Finding x- and y-intercepts of a Quadratic Function that Does Not Factor 

5. Determining x- and y-Intercepts of Functions 

6. Examples: Determining Intercepts

Graph Symmetry

1. Symmetry Around x-Axis, y-Axis, and Origin

2. Guided Practice: Testing for Symmetry Algebraically

Even and Odd Functions

1. What are Even and Odd Functions?

2. Determining if a Function is Even or Odd Using Graph Symmetry

3. Determining if a Function is Even or Odd Using Algebra

4. Guided Practice: Testing Algebraically Whether a Function is Even or Odd

Arithmetic of Functions

1. The Concept of Combining Functions Using Addition, Subtraction, Multiplication, or Division

2. Examples: Evaluating Functions That Have Been Combined Using Arithmetic

3. Arithmetically Combining Function Graphs

4. Arithmetically Combining Function Equations

5. Difference Quotient

6. Guided Practice: Determining the Difference Quotient for a Cubic Function

Composition of Functions

1. Understanding Composition of Functions with Numeric Examples

2. Determining the Domain of a Composition of Functions 

3. Examples: Determining the Composition of Two Functions and its Domain

4. Guided Practice: Determine the Composition and Domain of a Square Root Function with a Rational Function

5. Decomposing a Function

Linear Inequalities in Two Dimensions

1. Graphing Linear Inequalities in Two Dimensions

Linear Programming

1. Maximizing or Minimizing an Objective Function

2. Example: Maximize or Minimize an Objective Function

3. Linear Programming Example 1

4. Linear Programming Example 2

Polynomial Inequalities

1. Solving Polynomial Inequalities Using a Sign Chart

2. Guided Practice: Solving Polynomial Inequalities Using a Sign Chart

Rational Inequalities

1. Solving Rational Inequalities Using a Sign Chart

2. Guided Practice: Solving a Rational Inequality Using a Sign Chart

1. Exponent Review: Zero, Negative, and Fractional Exponents

Polynomial Terminology

1. Polynomial Terminology: Degree, Term, Coefficient

Adding, Multiplying, and Dividing Polynomials

1. Adding and Multiplying Polynomials 

2. Long Division of Polynomials

3. Synthetic Division of Polynomials

4. Evaluating a Polynomial Using Synthetic Division

Factoring

1. Factoring Refresher

2. The Definition of Factoring a Polynomial

3. Writing a Polynomial in Descending Order & Factoring out the Greatest Common Factor

4. Factoring Four Terms by Grouping

5. The Idea Behind Factoring Trinomials by Grouping

6. Examples: Factoring Trinomials by Grouping (ac-method)

7. More Examples: Factoring Trinomials by Grouping (ac-method)

8. Factoring a Perfect Square Trinomial 

9. Examples: Factoring Perfect Square Trinomials

10. Factoring a Binomial That is a Difference of Two Squares 

11. Examples: Factoring Binomials (Differences of Squares)

12. Basic Factoring Summary

13. Examples: Factoring Higher-Degree Polynomials Using Synthetic Division

Quadratic Polynomials

1. Solving Quadratic and Other Polynomial Equations by Factoring

2. Factoring a Polynomial Versus Solving a Polynomial Equation

3. General Method of Completing the Square

4. Solving a Quadratic Equation by Using a Square Root (Completing the Square)

5. A Formula for Solving Quadratic Equations (The Quadratic Formula)

6. Solving a Quadratic Equation Using the Quadratic Formula

7. Finding x- and y-intercepts of a Quadratic Function that Does Not Factor

8. Graphing a Quadratic Function in Standard Form By Using Symmetric Points

9. Examples of Graphing Quadratic Functions in Standard Form

10. Finding the Vertex of a Quadratic Function in Standard Form and then Determining if it is a Minimum or Maximum

11. Completing the Square to Write a Quadratic Function in Standard Form

12. The Vertex Formula for a Quadratic Function

13. An Application of the Vertex of a Quadratic Function 

Zeros and Factors of a Polynomial

1. Zeros and Linear Factors of a Polynomial

2. Building a Polynomial Whose Zeros are Rational

3. Building a Polynomial That Has Irrational Zeros

4. Building a Polynomial That Has Complex (Imaginary) Zeros

5. Guided Practice: Building a Polynomial Given Information about its Zeros

6. Finding Zeros of a Quadratic Polynomial

7. Possible Rational Zeros of a Polynomial 

8. Finding Rational, Irrational, and Complex Zeros of a Polynomial

9. Examples: Factoring Higher-Degree Polynomials Using Synthetic Division

Graphing Polynomial Functions Using End Behavior and Multiplicities of Zeros

1. Defining End Behavior

2. Examples: End Behavior of a Polynomial Function

3. Guided Practice: Determining the Leading Term and End Behavior of Polynomial Functions

4. Determining Zeros and Multiplicities of Polynomials that Factor

5. Determining What Values Make a Polynomial Zero, Positive, or Negative

6. Using End Behavior, Zeros, and Multiplicities to Determine Intervals Where a Polynomial is Positive or Negative

7. Guided Practice: Using End Behavior, Zeros, and Multiplicities to Make a Sign Chart for a Polynomial Function

8. Examples: Graphing Factored Polynomial Functions Using Zeros and End Behavior

9. Examples: Graphing Polynomial Functions that are not Factored

10. Guided Practice: Graphing a Polynomial Function Using its Number Line Chart

Polynomial Inequalities

1. Solving Polynomial Inequalities Using a Sign Chart

2. Guided Practice: Solving Polynomial Inequalities Using a Sign Chart

Basic Factoring

1. The Definition of Factoring a Polynomial

2. Writing a Polynomial in Descending Order & Factoring out the Greatest Common Factor

3. Factoring Four Terms by Grouping

4. The Idea Behind Factoring Trinomials by Grouping

5. Examples: Factoring Trinomials by Grouping (ac-method)

6. More Examples: Factoring Trinomials by Grouping (ac-method)

7. Factoring a Perfect Square Trinomial 

8. Examples: Factoring Perfect Square Trinomials

9. Factoring a Binomial That is a Difference of Two Squares 

10. Examples: Factoring Binomials (Differences of Squares)

11. Basic Factoring Summary

12. Factoring Refresher

13. Examples: Factoring Higher-Degree Polynomials Using Synthetic Division

1. Graphing a Constant Function on a Restricted Domain

2. Graphing a Linear Function on a Restricted Domain

3. Graphing a Quadratic Function on a Restricted Domain

4. Evaluating Piecewise-Defined Functions

5. Determining a Formula for a Piecewise-Defined Function Made up of Lines

6. Graphing a Piecewise-Defined Function

Rational Expressions and Complex Fractions

1. Zero in a Numerator or a Denominator

2. Negatives in Rational Expressions

3. Simplifying (or Reducing) Rational Expressions

4. Multiplying Rational Expressions

5. Dividing Rational Expressions

6. Finding the Least Common Denominator

7. Examples: Adding and Subtracting Rational Expressions

8. Simplifying Complex Fractions by Canceling Little Denominators

9. Simplifying Complex Fractions by Converting to Division

Graphing Rational Functions Using End Behavior and Multiplicities of Zeros

1. Determining Values that make a Rational Function Zero, Undefined, Positive, and Negative

2. Defining End Behavior

3. Examples: End Behavior of a Rational Function

4. Guided Practice: Determining the End Behavior of a Rational Function

5. End Behaviors of Polynomial & Rational Functions

6. Sketching a Rational Function Graph

7. Sketching a Rational Function Graph with a Hole

8. Sketching a Rational Function Graph with a Horizontal Asymptote

9. Rational Functions with Oblique Asymptotes

Rational Inequalities

1. Solving Rational Inequalities Using a Sign Chart

2. Guided Practice: Solving a Rational Inequality Using a Sign Chart

1. Perfect Powers

2. Defining Roots

3. The Radical Symbol

4. The Graphs of Basic Square Root and Cube Root Functions 

5. Simplifying Roots of Non-Perfect Powers

6. Rational (Fraction) Exponents

7. Adding and Subtracting Radicals

8. Multiplying and Distributing Radicals 

9. Rationalizing a Denominator with One Term

10. Rationalizing a Denominator with Two Terms Using the Conjugate

1. The Imaginary Number i and Raising it to a Power

2. Complex Numbers

3. Simplifying Square Roots Using the Imaginary Number i

4. Adding and Subtracting Complex Numbers

5. Multiplying Complex Numbers

6. Dividing Complex Numbers

1. Calculating the Distance Between Two Points (Ordered Pairs)

2. Finding One Coordinate of a Point Given the Distance Between that Point and Another Point

3. Graphing and Finding the Center and Radius of a Circle Given its Equation in Standard Form

4. Completing the Square to Write the Equation of a Circle in Standard Form

1. Expressions vs. Equations

2. Linear vs. Quadratic Equations 

Quadratic Equations

1. Solving Quadratic and Other Polynomial Equations by Factoring

2. Factoring a Polynomial Versus Solving a Polynomial Equation 

3. General Method of Completing the Square

4. Solving a Quadratic Equation by Using a Square Root (Completing the Square)

5. A Formula for Solving Quadratic Equations (The Quadratic Formula)

6. Solving a Quadratic Equation Using the Quadratic Formula 

Rational Equations

1. Solving Rational Equations by Clearing the Fractions 

2. Solving Rational Equations by Combining all Fractions

Radical Equations

1. Solving an Equation with One Radical

2. Solving an Equation with Multiple Radicals

3. Solving an Equation with Radicals that Results in a Quadratic Equation

Exponential Equations

1. Solving Exponential Equations

2. Guided Practice: Solving Exponential Equations

3. Solving Exponential Equations that Have Two Different Bases

Logarithmic Equations

1. Solving Logarithmic Equations

2. Guided Practice: Solving Log Equations

1. Definition of an Injective (One-to-One) Function

2. Definition of an Inverse Function with Basic Examples

3. Finding the Equation of an Inverse Function 

4. Guided Practice: Finding Equations of Inverse Functions

5. Using Function Composition to Verify that Two Functions are Inverses

6. Graphing an Inverse Function Using the Original Function Graph

1. Exponent Review: Zero, Negative, and Fractional Exponents 

2. Introduction to the Number e Using a Scientific Calculator

3. Graphing Parent Exponential Functions

4. Graphing Transformed Exponential Functions

5. Logarithmic and Exponential Functions are Inverses

6. Exponential and Logarithmic Functions "Undo" Each Other 

Logarithm Basics

1. Exponent Review: Zero, Negative, and Fractional Exponents

2. Introduction to Logarithms

Domain of a Logarithmic Function

1. Domain of a Log Function

Relationship Between Logarithmic Functions and Exponential Functions

1. Logarithmic and Exponential Functions are Inverses

2. Exponential and Logarithmic Functions "Undo" Each Other 

Graphing Logarithmic Functions

1. Graphing Parent Logarithmic Functions

2. Graphing Transformed Log Functions

3. Guided Practice: Using Transformations to Graph a Logarithmic Function

Logarithm Laws

1. What are Logarithm Laws?

2. Combining Logarithms into a Single Logarithm

3. Guided Practice: Using Logarithm Laws to Combine Logs

4. Expanding Logarithms

5. Guided Practice: Using Logarithm Laws to Expand a Log

1. Exponential Growth

2. Radioactive Decay

3. Newton's Law of Cooling

4. Exponential Application: Light Intensity

5. Continuously Compounding Interest

Using Matrices to Solve Systems of Equations

1. Solving Systems of Three Linear Equations Using Gaussian Elimination and Matrices

2. Solving a System of Three Equations Using its Augmented Matrix (Gauss-Jordan)

3. Guided Practice: Solving a System of Three Equations Using its Augmented Matrix (Gauss-Jordan)

Matrix Arithmetic

1. Matrix Scalar Multiplication

2. Matrix Addition and Subtraction

3. Guided Practice: Matrix Addition, Subtraction, and Scalar Multiplication

4. Matrix Multiplication

1. Using a Quadratic Model

2. Using an Exponential Model

3. Using a Logarithmic Model