Linear, Quadratic, Exponential Functions

Tim Brzezinski, 2016/12/28

目次

  1. Linear Functions vs. Exponential
    1. Exponential Growth vs. Linear Growth
    2. Linear Equation Anatomy
    3. Exponential Functions Anatomy
    4. Equation of a Line: Dynamic Illustrator
    5. Blueprint Equation of a Line (I)
    6. Graphing Linear Equations: Question Generator (V1)
    7. Graphing Linear Equations: Question Generator (V3)
    8. Graphing Linear Equations: Question Generator (V2)
    9. Graphing Linear Equations in Standard Form: Question Generator (V1)
    10. Working with Linear Equations Written in Standard Form: Quiz (V2-A)
    11. Working with Linear Equations Written in Standard Form: Quiz (V2-B)
    12. Payment Options!
    13. Exponential Functions: Graphs
    14. Exponential Growth & Decay (Illustrated Meaning)
    15. Half-Life Action!!!
    16. Animation 158
    17. Half-Life Action (2)!!!
    18. Half-Life Action (3)!!!
    19. Animation 159
  2. Construct Linear and Exponential Functions
    1. Identifying Slope and y-intercept (1)
    2. Graphing Linear Equations; Identifying Slope & y-intercept (With Hints)
    3. Graphing Linear Equations; Identifying Slope & y-intercept
    4. Linear Functions: Quick Modeling Templates
    5. Modeling Linear Growth
    6. Quiz: Modeling Linear Growth
    7. Quiz: Modeling Linear Growth (2)
    8. Graphing Linear Functions (1)
    9. Writing Linear Functions (1)
    10. Writing and Graphing Linear Functions (1)
    11. Graphing and Writing Linear Functions (2)
    12. Relating SLOPE and Y-INTERCEPT to the REAL WORLD
    13. Point-Slope Form: Quick Intro
    14. Point-Slope Form: Graphing Equations of Lines
    15. Writing the Equation of a Line Given a Slope & Point (V1)
    16. Open Middle Linear Functions Exercise
    17. Writing the Equation of a Line (I-VA)
    18. Writing Linear Equations (I) - B Obvious
    19. Writing Linear Equations Given Slope & Point (V2)
    20. Writing Linear Equations Given 2 Points (y-int = integer)
    21. Writing Linear Equations Given 2 Points (y-int not necessarily an integer)
    22. Quiz: Application Problems - Writing Linear Equations Given 2 Points
    23. Writing the Equation of a Line Given Both Intercepts
    24. Writing Equations of Parallel and Perpendicular Lines
    25. Modeling with Exponential Functions V1
    26. Modeling With Exponential Functions V2
    27. Exponential Functions: Graphs
    28. Half-Life Function
  3. Fastest Growing Function
    1. Fastest Growing Function?
  4. Modeling with Exponential Functions
    1. Exponential Functions Anatomy
    2. Quiz: Graphing Exponential Functions (Transformations Included)
    3. Modeling Exponential Growth & Decay: Quick Illustrator
    4. Exponential Growth & Decay: Quick Modeling Templates
    5. Exponential Growth vs. Decay: Quick Warm Up
    6. Quiz: Graphically Modeling Exponential Growth & Decay
    7. Writing Exponential Growth & Decay Function Models
    8. Exponential Growth and Decay: Modeling and Analyzing Graphically
    9. Compound Interest: What Happens as n Gets Larger?
    10. Compound Interest: Writing Function Models
    11. Compound Interest Question Generator (n= finite)
    12. Compound Interest Question Generator (Continuous Compounding)
    13. Half Life Modeling Exercises and Questions
    14. Quiz: Graphing Exponential Functions
    15. Solving Exponential Equations (I)
  5. Quadratic Functions
    1. Quadratic Functions Anatomy (1)
    2. Quadratic Functions Anatomy (2)
    3. Quadratic Functions Anatomy (3)
    4. Transforming Graphs of Quadratic Functions (1)
    5. Graphing Quadratic Functions
  6. Other Functions Resources
    1. Functions Resources

1.

Linear Functions vs. Exponential

  • 1. Exponential Growth vs. Linear Growth
  • 2. Linear Equation Anatomy
  • 3. Exponential Functions Anatomy
  • 4. Equation of a Line: Dynamic Illustrator
  • 5. Blueprint Equation of a Line (I)
  • 6. Graphing Linear Equations: Question Generator (V1)
  • 7. Graphing Linear Equations: Question Generator (V3)
  • 8. Graphing Linear Equations: Question Generator (V2)
  • 9. Graphing Linear Equations in Standard Form: Question Generator (V1)
  • 10. Working with Linear Equations Written in Standard Form: Quiz (V2-A)
  • 11. Working with Linear Equations Written in Standard Form: Quiz (V2-B)
  • 12. Payment Options!
  • 13. Exponential Functions: Graphs
  • 14. Exponential Growth & Decay (Illustrated Meaning)
  • 15. Half-Life Action!!!
  • 16. Animation 158
  • 17. Half-Life Action (2)!!!
  • 18. Half-Life Action (3)!!!
  • 19. Animation 159

1.1.

Exponential Growth vs. Linear Growth

"Linear functions grow by [color=#9900ff][b]equal differences[/b][/color] over equal intervals. [br]Exponential functions grow by [color=#9900ff][b]equal factors[/b][/color] over equal intervals."[br][br]Source: [url=http://www.corestandards.org/Math/Content/HSF/LE/]http://www.corestandards.org/Math/Content/HSF/LE/[/url][br][br][color=#cc0000][b]Check it out![/b][/color][br]Note the growth of the exponential function when its base is 2 and compare this growth to the exponential function with base of 3. (When you make the base = 3, you may want to zoom out before sliding the slider.) [br][br]
– Tim Brzezinski

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2.

Construct Linear and Exponential Functions

  • 1. Identifying Slope and y-intercept (1)
  • 2. Graphing Linear Equations; Identifying Slope & y-intercept (With Hints)
  • 3. Graphing Linear Equations; Identifying Slope & y-intercept
  • 4. Linear Functions: Quick Modeling Templates
  • 5. Modeling Linear Growth
  • 6. Quiz: Modeling Linear Growth
  • 7. Quiz: Modeling Linear Growth (2)
  • 8. Graphing Linear Functions (1)
  • 9. Writing Linear Functions (1)
  • 10. Writing and Graphing Linear Functions (1)
  • 11. Graphing and Writing Linear Functions (2)
  • 12. Relating SLOPE and Y-INTERCEPT to the REAL WORLD
  • 13. Point-Slope Form: Quick Intro
  • 14. Point-Slope Form: Graphing Equations of Lines
  • 15. Writing the Equation of a Line Given a Slope & Point (V1)
  • 16. Open Middle Linear Functions Exercise
  • 17. Writing the Equation of a Line (I-VA)
  • 18. Writing Linear Equations (I) - B Obvious
  • 19. Writing Linear Equations Given Slope & Point (V2)
  • 20. Writing Linear Equations Given 2 Points (y-int = integer)
  • 21. Writing Linear Equations Given 2 Points (y-int not necessarily an integer)
  • 22. Quiz: Application Problems - Writing Linear Equations Given 2 Points
  • 23. Writing the Equation of a Line Given Both Intercepts
  • 24. Writing Equations of Parallel and Perpendicular Lines
  • 25. Modeling with Exponential Functions V1
  • 26. Modeling With Exponential Functions V2
  • 27. Exponential Functions: Graphs
  • 28. Half-Life Function

2.1.

Identifying Slope and y-intercept (1)

– Tim Brzezinski

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3.

Fastest Growing Function

  • 1. Fastest Growing Function?

3.1.

Fastest Growing Function?

The applet below contains a collection of 6 functions.[br]Each function is color-coded so its graph is the same color as its description & equation listed on the right. [br][br][i]Of all these listed functions, which one will eventually "beat all the others", so to speak, with respect to increasing at the fastest rate? Explain your reasoning. [/i]
Quick (Silent) Demo
– Tim Brzezinski

4.

Modeling with Exponential Functions

  • 1. Exponential Functions Anatomy
  • 2. Quiz: Graphing Exponential Functions (Transformations Included)
  • 3. Modeling Exponential Growth & Decay: Quick Illustrator
  • 4. Exponential Growth & Decay: Quick Modeling Templates
  • 5. Exponential Growth vs. Decay: Quick Warm Up
  • 6. Quiz: Graphically Modeling Exponential Growth & Decay
  • 7. Writing Exponential Growth & Decay Function Models
  • 8. Exponential Growth and Decay: Modeling and Analyzing Graphically
  • 9. Compound Interest: What Happens as n Gets Larger?
  • 10. Compound Interest: Writing Function Models
  • 11. Compound Interest Question Generator (n= finite)
  • 12. Compound Interest Question Generator (Continuous Compounding)
  • 13. Half Life Modeling Exercises and Questions
  • 14. Quiz: Graphing Exponential Functions
  • 15. Solving Exponential Equations (I)

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– Tim Brzezinski

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Quadratic Functions

  • 1. Quadratic Functions Anatomy (1)
  • 2. Quadratic Functions Anatomy (2)
  • 3. Quadratic Functions Anatomy (3)
  • 4. Transforming Graphs of Quadratic Functions (1)
  • 5. Graphing Quadratic Functions

5.1.

Quadratic Functions Anatomy (1)

Interact with the app below by dragging the LARGE POINT. Then answer the questions that follow.
Suppose we graph the quadratic function [math]y=a\cdot x^2[/math]. [br][br]Which of the following statements are true? Check all that apply.
For the graph of [math]y=a\cdot x^2[/math], what happens when [math]a=0[/math]? Explain.
– Tim Brzezinski

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6.

Other Functions Resources

  • 1. Functions Resources

6.1.

Functions Resources

[list][*][b][url=https://www.geogebra.org/m/k6Dvu9f3]Interpreting Functions[/url][/b][/*][*][b][url=https://www.geogebra.org/m/uTddJKRC]Building Functions[/url][/b][/*][*][b][url=https://www.geogebra.org/m/GMvvpwrm]Linear, Quadratic, and Exponential Functions[/url][/b][/*][*][b][url=https://www.geogebra.org/m/aWuJMDas]Trigonometric Functions[/url][/b][/*][/list]
Half-life function: Quick Exploration. (Large point & slider moveable.)
What does it mean for a function to be odd? (Points moveable.)
– GeoGebra Team, Tim Brzezinski

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