Algebra and Trigonometry: Functions

• Instructor Introduction

• Course Curriculum

• Road Map

• How to Best Use This Course

• Feedback

• Legal Disclaimer

• Course Introduction

• Introduction to Functions (Part 1 of 2)

• Introduction to Functions (Part 2 of 2)

• How to Determine If a Relation a Function - Exercise

• Function Notation

• Representing Functions Using Tables

• Finding Input and Output Values of a Function

• Evaluating Functions - Exercise

• Evaluating a Function Expressed in Formulas

• Evaluating a Function Given in Tabular Form

• Finding Function Values from a Graph

• Determining Whether a Function is One-to-One

• Vertical Line Test

• Horizontal Line Test

• Basic Toolkit Functions (Part 1 of 3)

• Basic Toolkit Functions (Part 2 of 3)

• Basic Toolkit Functions (Part 3 of 3)

• Domain and Range Introduction

• Interval Notation Summery

• Finding the Domain of a Function - Exercise

• Inequality, Set-builder and Interval Notations

• Describing Set on the Real-Number Line

• Finding Domain and Range From Graphs

• Finding Domains and Ranges of the Toolkit Functions

• Finding the Domain and Range of Functions - Exercise

• Piecewise-Defined Functions

• Working with a Piecewise Function - Exercise

• Graphing a Piecewise Function - Exercise

• Rate of Change Introduction

• Rate of Change Formula and Example

• Computing an Average Rate of Change based on a Table

• Computing an Average Rate of Change based on a Function Graph

• Computing an Average Rate of Change based on a Function Formula

• Computing an Average Rate of Change - Example

• Increasing, Decreasing, Local Minimum, Maximum, Extrema - Part 1

• Increasing, Decreasing, Local Minimum, Maximum, Extrema - Part 2

• Finding Increasing and Decreasing Intervals on a Graph

• Finding Extrema of a Function using Technology

• Finding the Local Maximum and Local Minimum of a Function - Example

• Analyzing the Toolkit Functions for Increasing and Decreasing Intervals

• Absolute Minimum and Absolute Maximum of a Function

• Finding the Absolute Minima and Maxima of a Function - Example

• Composition of Functions - Concept

• Combining Functions Using Algebraic Operations

• Combining Functions Using Algebraic Operations - Example

• Composition of Functions - Concept and Mathematical Notation

• Composition of Functions Not Commutative - Exercise

• Composition of Functions - Exercise

• Evaluating Composite Functions Using Tables

• Evaluating Composite Functions Using Graphs

• Evaluating Composite Functions Using Function Formulas

• Finding the Domain of a Composite Function - Part 1

• Finding the Domain of a Composite Function - Part 2

• Finding the Domain of a Composite Function - Exercise

• Decomposing Composite Functions

• Transformation of Functions - Introduction

• Vertical Transformation of Functions

• Vertical Shift - Example

• Horizontal Shift of Functions

• Horizontal Shift to Right and Left - Part 1

• Horizontal Shift to Right and Left - Part 2

• Horizontal Shift - Example

• Inside and Outside Changes Affecting Domain or Range

• Shifting a Tabular Function Horizontally

• Identifying a Horizontal Shift of a Toolkit Function

• Horizontal Function shift - Example

• Graphing Combined Vertical and Horizontal Shifts - Example

• Identifying Combined Horizontal and Vertical Shifts - Example

• Transformation of Functions - Example

• Reflecting Function About the x and y axes - Introduction

• Reflecting a Graph Horizontally and Vertically - Example

• Reflecting a Tabular Function Horizontally and Vertically - Example

• Applying a Learning Model Equation - Example

• Graphing the Vertical and Horizontal Transformations of a Toolkit Function

• Even and Odd Functions - Part 1

• Even and Odd Functions - Part 2

• Even and Odd Functions - Example

• Vertical and Horizontal Compression and Stretches - Part 1

• Vertical and Horizontal Compression and Stretches - Part 2

• Vertical and Horizontal Compression and Stretches - Part 3

• Vertical Stretch of Functions and Example

• Finding a Vertical Compression of a Tabular Function

• Recognizing a Vertical Stretch - Example

• Function Formula Transformation - Example

• Horizontal Compression and Stretches - Concept

• Graphing a Horizontal Compression - Example

• Finding a Horizontal Stretch for a Tabular Function

• Recognizing a Horizontal Compression on a Graph

• Finding the Formula for a Stretched Toolkit Function

• Performing a Sequence of Transformations

• Finding a Triple Transformation of a Tabular Function - Example

• Finding a Triple Transformation of a Graph

• Absolute Value Function - Introduction

• Absolute Value - Example

• Graphing an Absolute Value Function

• Writing an Equation for an Absolute Value Function Given a Graph

• Absolute Value Function Transformation - Example

• Finding the Zeros of an Absolute Value Function - Example

• Solving an Absolute Value Equation

• Inverse Functions - Introduction

• Domain, Codomain, Range and Image of a Function

• One-to-one or Injective Functions

• Onto or Surjective Functions

• Bijective or One-to-one Correspondence Functions

• Identifying an Inverse Function for a Given Input-Output Pair - Example

• Original and Inverse Functions Input-Output Pairs

• Testing Inverse Relationships Algebraically - Example

• Finding the Domain and Range of Inverse Functions

• Finding the Inverse of Toolkit Functions - Part 1

• Finding the Inverse of Toolkit Functions - Part 2

• Inverting Tabular Functions

• Evaluating a Function and its Inverse from a Graph at Specific Points

• Finding Inverses of Functions Represented by Formulas - Part 1

• Finding Inverses of Functions Represented by Formulas - Part 2

• Inverting the Fahrenheit-to-Celsius Function - Example

• Solving to Find an Inverse Function

• Solving to Find an Inverse with Radicals

• Finding the Inverse of a Function Using Reflection about the Identity Line