CCSS High School: Functions (Linear, Quadratic, Exponential)

Tim Brzezinski, mark vasicek, May 6, 2018

[b][color=#1551b5]This GeoGebra Book contains discovery-based learning activities, investigations, and meaningful remediation worksheets that were designed to help enhance students' learning of concepts related to Functions: Linear, Quadratic, and Exponential Models. [/color][/b]

Table of Contents

  1. HSF.LE.A.1, 1.A, 1.B, 1.C
    1. Equation of a Line: Dynamic Illustrator
    2. Blueprint Equation of a Line (I)
    3. Graphing Linear Equations: Question Generator (V1)
    4. Graphing Linear Equations: Question Generator (V3)
    5. Graphing Linear Equations: Question Generator (V2)
    6. Graphing Linear Equations in Standard Form: Question Generator (V1)
    7. Working with Linear Equations Written in Standard Form: Quiz (V2-A)
    8. Working with Linear Equations Written in Standard Form: Quiz (V2-B)
    9. Payment Options!
    10. Exponential Functions: Graphs
    11. Exponential Growth vs. Linear Growth
    12. Exponential Growth & Decay (Illustrated Meaning)
    13. Half-Life Action!!!
    14. Animation 158
    15. Half-Life Action (2)!!!
    16. Half-Life Action (3)!!!
    17. Animation 159
  2. HSF.LE.A.2
    1. Relating SLOPE and Y-INTERCEPT to the REAL WORLD
    2. Writing the Equation of a Line (I-VA)
    3. Writing Linear Equations (I) - B Obvious
    4. Writing the Equation of a Line Given a Slope & Point (V1)
    5. Writing Linear Equations Given Slope & Point (V2)
    6. Writing Linear Equations Given 2 Points (y-int = integer)
    7. Writing Linear Equations Given 2 Points (y-int not necessarily an integer)
    8. Quiz: Application Problems - Writing Linear Equations Given 2 Points
    9. Writing the Equation of a Line Given Both Intercepts
    10. Writing Equations of Parallel and Perpendicular Lines
    11. Modeling with Exponential Functions V1
    12. Modeling With Exponential Functions V2
    13. Exponential Functions: Graphs
    14. Half-Life Function
  3. HSF.LE.A.3
    1. Fastest Growing Function?
  4. HSF.LE.A.4
    1. Solving Exponential Equations (I)
  5. HSF.LE.B.5
    1. Relating SLOPE and Y-INTERCEPT to the REAL WORLD
  6. Links to Other CCSS High School: Functions Resources
    1. Functions Resources
  7. *Additional: Links to CCSS High School: Geometry Resources
    1. Geometry Resources

1.

HSF.LE.A.1, 1.A, 1.B, 1.C

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

1.1.

Equation of a Line: Dynamic Illustrator

How are the parameters (i.e. coefficients) of the terms on the right side of the equation of the line made visible in the graph itself? Explain.
Quick (Silent) Demo
– Tim Brzezinski

1.2.

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1.3.

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1.4.

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1.5.

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1.6.

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1.7.

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1.8.

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1.9.

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1.10.

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1.11.

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1.12.

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1.13.

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1.14.

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1.15.

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1.16.

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1.17.

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2.

HSF.LE.A.2

  • 1. Relating SLOPE and Y-INTERCEPT to the REAL WORLD
  • 2. Writing the Equation of a Line (I-VA)
  • 3. Writing Linear Equations (I) - B Obvious
  • 4. Writing the Equation of a Line Given a Slope & Point (V1)
  • 5. Writing Linear Equations Given Slope & Point (V2)
  • 6. Writing Linear Equations Given 2 Points (y-int = integer)
  • 7. Writing Linear Equations Given 2 Points (y-int not necessarily an integer)
  • 8. Quiz: Application Problems - Writing Linear Equations Given 2 Points
  • 9. Writing the Equation of a Line Given Both Intercepts
  • 10. Writing Equations of Parallel and Perpendicular Lines
  • 11. Modeling with Exponential Functions V1
  • 12. Modeling With Exponential Functions V2
  • 13. Exponential Functions: Graphs
  • 14. Half-Life Function

2.1.

Relating SLOPE and Y-INTERCEPT to the REAL WORLD

Link to [color=#0000ff][b][url=https://docs.google.com/document/d/19m3Q8iAKTHopwKct2QsGpOfy1AoLrUH2YNi-xXm6yJc/copy]Relating SLOPE and Y-INTERCEPT to the REAL WORLD[/url][/b][/color][br]
– Tim Brzezinski

2.2.

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2.3.

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2.4.

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2.5.

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2.6.

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2.7.

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2.8.

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2.9.

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2.10.

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2.11.

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2.12.

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2.13.

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2.14.

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3.

HSF.LE.A.3

  • 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.

HSF.LE.A.4

  • 1. Solving Exponential Equations (I)

4.1.

Solving Exponential Equations (I)

[b][color=#cc0000]Directions:[/color] [br][br]1) Solve the given exponential equation you see on the right side of the applet. [br]2) Write an exact expression for the solution to this equation. (It should be written as a logarithm.)[br]3) Use your calculator to obtain an approximate decimal value of this solution [br] (Round this value to the nearest 0.01).[/b][br][br]4) [b]Check the reasonableness of your solution by determining the coordinates (x, y) of the [br] intersection of graphs[/b] [i][color=#0000ff][b]f[/b][/color][/i] [b]and[/b] [i][color=#9900ff][b]g[/b][/color][/i][b].[/b] [br][br][i][color=#1e84cc]Generate as many examples as you need and work through these examples in order to master this concept! [br][/color][/i][br][color=#cc0000][b]Note:[/b][/color] [br]For some generated problems, you may need to [color=#cc0000][b]ZOOM WAY IN[/b][/color] or [color=#cc0000][b]ZOOM WAY OUT[/b][/color] in order to see the point of intersections of graphs [i][color=#0000ff][b]f[/b][/color][/i] and [i][color=#9900ff][b]g[/b][/color][/i].
– Tim Brzezinski

5.

HSF.LE.B.5

  • 1. Relating SLOPE and Y-INTERCEPT to the REAL WORLD

5.1.

– Tim Brzezinski

6.

Links to Other CCSS High School: 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

7.

*Additional: Links to CCSS High School: Geometry Resources

  • 1. Geometry Resources

7.1.

Geometry Resources

[list][*][b][url=https://www.geogebra.org/m/z8nvD94T]Congruence (Volume 1)[/url][/b][/*][*][b][url=https://www.geogebra.org/m/munhXmzx]Congruence (Volume 2)[/url][/b][/*][*][b][url=https://www.geogebra.org/m/dPqv8ACE]Similarity, Right Triangles, Trigonometry[/url][/b][/*][*][b][url=https://www.geogebra.org/m/C7dutQHh]Circles[/url][/b][/*][*][b][url=https://www.geogebra.org/m/K2YbdFk8]Coordinate and Analytic Geometry[/url][/b][/*][*][b][url=https://www.geogebra.org/m/xDNjSjEK]Area, Surface Area, Volume, 3D, Cross Section[/url] [/b][/*][*][b][url=https://www.geogebra.org/m/NjmEPs3t]Proof Challenges[/url]  [/b][/*][/list]
What phenomenon is dynamically being illustrated here? (Vertices are moveable.)
What phenomenon is dynamically being illustrated here? (Vertices are moveable.)
– Tim Brzezinski

Information