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)

  • continuity

• 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

x- & y-intercepts

pos/neg intervals and zeros

max/min and increasing/decreasing intervals

average rate of change

inflection points and concavity

odd/even symmetry

bounded

HA & VA

• Explanation:

  • Notes | Annotated

  • Khan video: Graphing shifted functions

  • Khan video: Shifting functions

  • Khan video: Compressing functions

  • Khan video: Reflecting & compressing functions

  • f(|x|) vs |f(x)|

• 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

Explanation:

• • Notes | Annotated

  • Videos:  

  • Real meaning of MPH

    • Khan video: Finding the slope of a line from its graph 

      • optional: Slope and rate of change | Graphical slope of a line

  • Khan video: Slope from two ordered pairs example 1 

    • • optional: Slope from two ordered pairs example 2

  • Khan video: Interpreting linear tables word problems example 1

    • Khan video: Intuitive understanding of slope example

Practice Problems:

• • Khan Exercise: Slope from a graph

  • Khan Exercise: Slope from two solutions (points) Hint: type everything into the graphing calculator; press Enter, then press Math, select 1:Frac, and Enter;

  • example (17.4-23.5)/(4.1-6.2)

  • Worksheet #1 

  • Worksheet #2 | Answers

Explanation:

• • Notes | Annotated

  • Khan video: Point-slope and slope-intercept form from two points

  • Khan video: Writing equations in all forms

  • Khan review: Point-slope form review

Practice Problems:

• • Khan Exercise: Point-slope form

  • Worksheet #1 

  • Worksheet #2 | Answers

Explanation:

• • Notes | Annotated

  • Khan videos: Example: Write the equation of a perpendicular line (Example 2)

Practice Problems:

• • Khan Practice - Equations of parallel and perpendicular lines 

  • Worksheet #1 | Answers

  • Vocabulary Review

Explanation:

• • Notes 

  • Khan video: Fitting a line to data (using Excel)

  • Khan video (for the writing prompt):  Predicting Linear Models

  • Khan video: Correlation and causality

  • Spreadsheets for linear modeling

    • Desmos.com (click the question mark in the upper right-hand corner then Regressions for a brief tutorial).  Basically, press + and select the table.  Then type in the table values.  Next press + and select the expression. Then type y1~mx1+b. Here is a shortcut to the regression tutorial.

    • Texas Instrument Graphing Calculators

    • Google Sheets (the instructions are for after you create a table and scatterplot). 

    • Khan video on using Excel

    • Numbers

Practice Problems:

• • Worksheet #1

• • Khan Exercise: Eyeballing the line of best fit (Estimating the line of best-fit exercise)

  • Khan Exercise: Correlation coefficient intuition

  • Online activity: Line of Best Fit by Illuminations (Java)

Explanations:

• • Notes | Annotated

  • Notes | Annotated

  • Khan video: Introduction to piecewise functions

  • Khan video: How to evaluate a piecewise function from its formula or graph (example)

  • Desmos: Graph of the greatest integer function

  • Youtube video #1

  • Youtube video #2

  • 2023 tax bracket for single person

Practice Problems:

• • Desmos Activity: Lava and Piecewise Functions (teacher use only)

  • Worksheet #1 

  • Worksheet #2

  • Worksheet #1

  • Worksheet #2 | Answers

  • Khan Exercise: Evaluate piecewise functions

  • Khan Exercise: Evaluate step functions from their graph

  • Khan Exercise: Piecewise functions graphs