Functions

1) Domain and Range of Graphs with Interval Notation & Set Builder

• • Explanation:

    • Notes | Annotated

    • Videos

      • Khan: Intervals and interval notation

      • Khan: What is the domain of a function?

    • Khan: Worked example: domain and range from graph

  • Practice

  • Worksheet #1

  • Worksheet #2

    • Khan Exercise: Domain and range from graph

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

2) Domain of Rational Functions (vertical asymptotes and removable discontinuity)

• • Explanation:

    • Notes | Annotated

    • Video:

    • Why Dividing by Zero is Undefined

    • Why Zero Divided by Zero is Undefined/Indeterminate

      • Khan: Discontinuities of rational functions

  • Practice Problems:

    • Worksheet #1 | Answers

  • Worksheet #2

  • Worksheet #3

  • Comparing the Graph of Basic Rational Functions WS

    • Khan Exercise: Rational function points of discontinuity

3) Domain of Root and Logarithmic Functions

• • Explanation:

    • Notes | Annotated

    • Video:

    • Roots

      • Khan: Domain of a radical function

    • Practice:

      • Khan: Determine the domain of functions

      • Worksheet #1 | Answers

    • Worksheet #2

    • Worksheet #3

4) Domain of Rational Functions with Roots

• • Explanation:

    • Notes | Annotated

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

  • Practice Problems:

    • Worksheet | Answers

5) Function Families

• Explanation:

  • Notes on the domain of function families | Annotated

  • Online Flashcards - memorize the shape of function families

  • Khan video: Graphs of logarithms & exponentials

    • Khan video: Graphing basic logarithmic functions

• 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)

6) Special piecewise functions: absolute value & greatest integer function

• • Explanation:

    • Notes | Annotated

    • Desmos: Graph of the greatest integer function

  • Practice Problems:

  • Worksheet

7) Transformation of functions: scale factors, reflections, and shifts

• • Explanation:

    • Notes Annotated

    • Graph by transformation:

      • Khan video: Graphing shifted functions

    • From one function to another:

      • Khan video: Shifting functions

      • Khan video: Compressing functions

      • Khan video: Reflecting & compressing functions

  • Practice Problems:

  • Worksheet #1

  • Worksheet #2

    • Khan Exercise: Graph quadratics: vertex form

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

    • Khan Exercise: Transforming functions

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

8) Transformation of Piecewise Graphs

• • Explanation:

    • Notes | Annotated

  • Practice Problems

  • Worksheet #1

  • Worksheet #2

  • Worksheet #3

  • AP Calc style question for Precalculus

    • Khan Exercise: Transforming functions

    • Desmos: Transforming the Graph of Piecewise Functions

9) Absolute value of a Function

• • Explanation:

  • Notes

  • Practice Problems:

  • Worksheet #1

10) Review Graphing Functions by Transformations and Domain of Functions

• Review WS #1

11) Graphing Relations

12) Basic Operations with Functions (Add, Subtract, Multiply, and Divide)

• • 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

  • Practice Problems:

  • Worksheet #1

  • Worksheet #2

    • Khan Article: Intro to combining functions

    • Khan article: Multiplying & dividing functions

    • Khan exercise: Model with function combination

13) Composite Functions

• • Explanation:

    • Notes | Annotated

    • Khan text and checking (application): Intro to composing functions

    • Khan text and checking (functions and numbers): Composing functions

    • Khan video (an example with numerical input): Evaluating composite functions

    • Khan video: Evaluating composite functions: using tables

    • Khan video: Finding composite functions

  • Practice Problems

  • Worksheet #1

  • Worksheet #2

  • Worksheet #3

    • Khan Exercise (numerical input): Evaluate composite functions

    • Khan Exercise: Find composite functions

14) Advanced Composite Functions and Mixed Review of Operations & Modeling

• • Mixed Review

    • Notes | Annotated Notes

    • Khan video: Modeling with composite functions

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

  • Practice Problems:

  • Worksheet #3

    • Khan exercise: Model with composite functions

15) Finding Inverse Functions

• • 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 text and checking: Finding inverse functions

  • Practice problems:

  • Worksheet #1

  • Worksheet #3

    • Khan exercise: Find inverse functions

16) Verifying Inverse Functions and graphs

• • Explanation:

    • Notes | Annotated

    • Khan text and checking: Intro to inverse functions

    • 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 text and checking: Verifying inverse functions by composition

  • Practice Problems:

  • Worksheet #3

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

    • Khan Exercise: Verify inverse functions

16b) Determining whether a function is invertible

• Explanation:

  • Khan video: Determining if a function is invertible

    • Khan text and checking: Intro to invertible functions

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

• Practice Problems:

  • Khan exercise: Determine if a function is invertible

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

17) All Operations on Functions Given a Graph

• • Explanation

    • Notes | Annotated

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

    • Khan video: Evaluating composite functions: using graphs

  • Practice Problems:

    • Worksheet

    • 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

18) Review

• Worksheet #1

  • Worksheet #2 | Answers