Algebra and Trigonometry: Functions

Course Curriculum

Chapter 1: 3.0 – Introduction

Lecture 1: Instructor Introduction

Lecture 2: Course Curriculum

Lecture 3: Road Map

Lecture 4: How to Best Use This Course

Lecture 5: Feedback

Lecture 6: Legal Disclaimer

Chapter 2: 3.1 – Functions and Function Notation

Lecture 1: Course Introduction

Lecture 2: Introduction to Functions (Part 1 of 2)

Lecture 3: Introduction to Functions (Part 2 of 2)

Lecture 4: How to Determine If a Relation a Function – Exercise

Lecture 5: How to Determine If a Relation a Function – Exercise

Lecture 6: Function Notation

Lecture 7: Representing Functions Using Tables

Lecture 8: Finding Input and Output Values of a Function

Lecture 9: Evaluating Functions – Exercise

Lecture 10: Evaluating a Function Expressed in Formulas

Lecture 11: Evaluating a Function Given in Tabular Form

Lecture 12: Finding Function Values from a Graph

Lecture 13: Determining Whether a Function is One-to-One

Lecture 14: Vertical Line Test

Lecture 15: Horizontal Line Test

Lecture 16: Basic Toolkit Functions (Part 1 of 3)

Lecture 17: Basic Toolkit Functions (Part 2 of 3)

Lecture 18: Basic Toolkit Functions (Part 3 of 3)

Chapter 3: 3.2 – Domain and Range

Lecture 1: Domain and Range Introduction

Lecture 2: Interval Notation Summery

Lecture 3: Finding the Domain of a Function – Exercise

Lecture 4: Finding the Domain of a Function – Exercise

Lecture 5: Inequality, Set-builder and Interval Notations

Lecture 6: Describing Set on the Real-Number Line

Lecture 7: Finding Domain and Range From Graphs

Lecture 8: Finding Domains and Ranges of the Toolkit Functions

Lecture 9: Finding the Domain and Range of Functions – Exercise

Lecture 10: Piecewise-Defined Functions

Lecture 11: Working with a Piecewise Function – Exercise

Lecture 12: Graphing a Piecewise Function – Exercise

Chapter 4: 3.3 – Rates of Change and Behavior of Graphs

Lecture 1: Rate of Change Introduction

Lecture 2: Rate of Change Formula and Example

Lecture 3: Computing an Average Rate of Change based on a Table

Lecture 4: Computing an Average Rate of Change based on a Function Graph

Lecture 5: Computing an Average Rate of Change based on a Function Formula

Lecture 6: Computing an Average Rate of Change – Example

Lecture 7: Increasing, Decreasing, Local Minimum, Maximum, Extrema – Part 1

Lecture 8: Increasing, Decreasing, Local Minimum, Maximum, Extrema – Part 2

Lecture 9: Finding Increasing and Decreasing Intervals on a Graph

Lecture 10: Finding Extrema of a Function using Technology

Lecture 11: Finding the Local Maximum and Local Minimum of a Function – Example

Lecture 12: Analyzing the Toolkit Functions for Increasing and Decreasing Intervals

Lecture 13: Absolute Minimum and Absolute Maximum of a Function

Lecture 14: Finding the Absolute Minima and Maxima of a Function – Example

Chapter 5: 3.4 – Composition of Functions

Lecture 1: Composition of Functions – Concept

Lecture 2: Combining Functions Using Algebraic Operations

Lecture 3: Combining Functions Using Algebraic Operations – Example

Lecture 4: Composition of Functions – Concept and Mathematical Notation

Lecture 5: Composition of Functions Not Commutative – Exercise

Lecture 6: Composition of Functions – Exercise

Lecture 7: Composition of Functions – Exercise

Lecture 8: Evaluating Composite Functions Using Tables

Lecture 9: Evaluating Composite Functions Using Graphs

Lecture 10: Evaluating Composite Functions Using Function Formulas

Lecture 11: Finding the Domain of a Composite Function – Part 1

Lecture 12: Finding the Domain of a Composite Function – Part 2

Lecture 13: Finding the Domain of a Composite Function – Exercise

Lecture 14: Decomposing Composite Functions

Chapter 6: 3.5 – Transformation of Functions

Lecture 1: Transformation of Functions – Introduction

Lecture 2: Vertical Transformation of Functions

Lecture 3: Vertical Shift – Example

Lecture 4: Vertical Shift – Example

Lecture 5: Horizontal Shift of Functions

Lecture 6: Horizontal Shift to Right and Left – Part 1

Lecture 7: Horizontal Shift to Right and Left – Part 2

Lecture 8: Horizontal Shift – Example

Lecture 9: Inside and Outside Changes Affecting Domain or Range

Lecture 10: Shifting a Tabular Function Horizontally

Lecture 11: Identifying a Horizontal Shift of a Toolkit Function

Lecture 12: Horizontal Function shift – Example

Lecture 13: Graphing Combined Vertical and Horizontal Shifts – Example

Lecture 14: Identifying Combined Horizontal and Vertical Shifts – Example

Lecture 15: Transformation of Functions – Example

Lecture 16: Reflecting Function About the x and y axes – Introduction

Lecture 17: Reflecting a Graph Horizontally and Vertically – Example

Lecture 18: Reflecting a Graph Horizontally and Vertically – Example

Lecture 19: Reflecting a Tabular Function Horizontally and Vertically – Example

Lecture 20: Applying a Learning Model Equation – Example

Lecture 21: Graphing the Vertical and Horizontal Transformations of a Toolkit Function

Lecture 22: Even and Odd Functions – Part 1

Lecture 23: Even and Odd Functions – Part 2

Lecture 24: Even and Odd Functions – Example

Lecture 25: Vertical and Horizontal Compression and Stretches – Part 1

Lecture 26: Vertical and Horizontal Compression and Stretches – Part 2

Lecture 27: Vertical and Horizontal Compression and Stretches – Part 3

Lecture 28: Vertical Stretch of Functions and Example

Lecture 29: Finding a Vertical Compression of a Tabular Function

Lecture 30: Recognizing a Vertical Stretch – Example