Functions

• Explanation:

  • Khan video: Intervals and interval notation

  • Khan video: What is the domain of a function?

  • Khan video: Worked example: domain and range from graph

  • Khan video: Why Dividing by Zero is Undefined

  • Khan video: Why Zero Divided by Zero is Undefined/Indeterminate

  • Khan video: Discontinuities of rational functions

  • Khan video: Worked example: domain of algebraic functions (only the first example)

• Practice:

  • Worksheet #1

  • Comparing the Graph of Basic Rational Functions WS

  • Khan Exercise: Domain and range from graph

• • Khan Exercise: Determine the domain of functions

• • Khan Exercise: Domain of a radical function

  • Amplify Activity: Domain and Range Introduction (Teacher Use)

Explanation:

• Online Flashcards - memorize the shape of function families

Practice Problems:

• Graphing Functions Families by Hand WS

• Analyzing the Characteristics of Function Families WS

  • Desmos Activity: Exponential and Logarithmic Functions (teacher use only)

  • Desmos Activity: Card Match Function Families (teacher use only)  - includes logs

• Explanation:

  • Notes | Annotated

  • Khan video: Graphing shifted functions

  • Khan video: Shifting functions

  • Khan video: Compressing functions

  • Khan video: Reflecting & compressing functions

• Practice Problems:

  • Worksheet #1

  • Khan Exercise: Shift functions (includes some stretch and compression)

  • Khan Exercise: Transforming functions

  • Amplify Activity: graph by transformations (teacher use only)

• • AP Calc style question for Precalculus

  • Khan Exercise: Transforming functions

  • Khan Exercise: Graph quadratics: vertex form

  • Amplify: Transforming the Graph of Piecewise Functions

• Explanation:

  • Notes | Annotated

  • Khan video: Evaluating composite functions

  • Khan video: Evaluating composite functions (advanced)

  • Khan video: Evaluating composite functions: using tables

  • Khan video: Evaluating composite functions: using graphs

  • Khan video: Finding composite functions

  • Khan video: Modeling with composite functions

  • Khan video: Modeling with composite functions: skydiving

  • Khan video: Model with composite functions

• Practice Problems

  • Worksheet #1

  • Khan Article (functions and numbers): Composing functions - assign

  • Khan Exercise: Evaluate composite functions

  • Khan Exercise: Evaluate composite functions: graphs & tables

  • Khan Exercise: Find composite functions - no need to simplify

  • Khan Article: Intro to composing functions - assign with videos for extra credit

  • Khan Exercise: Model with composite functions - extra credit

• Explanation

  • Notes | Annotated

  • Khan video: Inputs & outputs of inverse functions

  • Khan video: Finding inverse functions: linear

  • Khan video: Finding inverse functions: radical

  • Khan video: Finding inverse functions: rational (the answer has a mistake; it should be (-1-3x)/(x-2)

  • Khan video: Graphing the inverse of a linear function

  • Khan video: Verifying inverse functions by composition

  • Khan video: Verifying inverse functions by composition: not inverse

  • Khan article: Finding inverse functions

  • Khan video: Determining if a function is invertible

  • Khan article: Intro to invertible functions

  • Khan video: Restricting domains of functions to make them invertible

• Practice problems: 

  • Worksheet #1

  • Khan exercise: Find inverse functions

  • Khan article: Intro to inverse functions

  • Khan article: Verifying inverse functions by composition

  • Khan exercise: Evaluate inverse functions (includes tables, equations, and graphs)

  • Khan exercise: Verify inverse functions

  • Khan exercise: Determine if a function is invertible

  • Khan exercise: Restrict domains of functions to make them invertible

• Explanation:

  • Notes | Annotated

  • Khan video: Adding functions

  • Khan video: Subtracting functions

  • Khan video: Multiplying functions

  • Khan video: Dividing functions

  • Khan video: Modeling with function combination

  • Notes | Annotated Notes 

  • Khan video: Modeling with composite functions

  • Khan video: Modeling with composite functions (example 2)

  • Khan Video: How to evaluate an expression that contains function notation (example)

  • Khan video: Evaluating composite functions: using graphs

• Practice Problems:

  • Worksheet #1

  • Khan Article: Intro to combining functions

  • Khan article: Multiplying & dividing functions

  • Khan exercise: Model with function combination

  • Worksheet #3

  • Khan exercise: Model with composite functions

  • Khan Exercise: Evaluating function expressions

  • Khan Exercise: Evaluate composite functions: graphs & tables

  • MathPlotter: Function Operations: graphically find the sum of two functions with the use of sliders