CCSS High School: Functions (Building Functions)

Tim Brzezinski, SAVAŞ ORHAN, Mar 25, 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 building functions. [/color] [/b]

Table of Contents

  1. HSF.BF.A.1, A.1.A
    1. Relating SLOPE and Y-INTERCEPT to the REAL WORLD
    2. Writing the Equation of a Line (I-VA)
    3. Quiz: Modeling with Linear Functions
    4. Writing the Equation of a Line Given a Slope & Point (V1)
    5. Composition of Functions: Algebraic (Quiz)
    6. Writing Linear Equations Given Slope & Point (V2)
    7. Writing Linear Equations Given 2 Points (y-int = integer)
    8. Writing Linear Equations Given 2 Points (y-int not necessarily an integer)
    9. Quiz: Application Problems - Writing Linear Equations Given 2 Points
    10. Writing the Equation of a Line Given Both Intercepts
    11. Writing Equations of Parallel and Perpendicular Lines
    12. Equation of a Line: Dynamic Illustrator
    13. Half-Life Function
    14. Animation 159
    15. Quiz: Writing Exponential Growth & Decay Functions
    16. Box with Open Top
  2. HSF.BF.A.1.B, A.1.C
    1. Relating SLOPE and Y-INTERCEPT to the REAL WORLD
    2. Quiz: Modeling with Linear Functions
    3. Application Problems: Solving Linear Equations (1)
    4. Perimeter of a Rectangle: Solving Linear Equations
    5. Application Problems: Solving Linear Equations (3)
    6. Friends and Money: Solving Linear Equations
    7. Application Problems: Solving Linear Equations (5)
    8. Function Composition: Dynamic Illustrator (1)
    9. Function Composition: Dynamic Illustrator (2)
    10. Animation 157
    11. Composition of Functions: Algebraic (Quiz)
    12. Quiz: Composition of Functions (Graph & Table)
    13. Composition of Functions: Graphical (Quiz) - V1
  3. HSF.BF.A.2
    1. AQR Section 21: Arithmetic or Geometric?
  4. HSF.BF.B.3
    1. Function Transformations
    2. Transformations of Graphs (a, h, k)
    3. What Makes a Function Even?
    4. Animation 143
    5. What Makes a Function Odd?
    6. Animation 144
    7. Odd Functions (Another Look)
    8. Odd Functions: Another Look (Take 2)!
  5. HSF.BF.B.4, 4.A, 4.B, 4.C, 4.D
    1. Inverse Relations: Graphs
    2. Writing Inverse Functions: Quiz (1)
    3. Writing Inverse Functions: Quiz (2)
    4. Writing Inverse Functions: Quiz (3)
    5. Graphing Inverse Functions: Quiz (1)
  6. HSF.BF.B.5
    1. Logarithmic Action!
    2. Logarithmic Action (2)!
    3. Logarithmic Action (3)!
    4. Logarithmic Action (4)!
    5. Logarithmic Action (4)! V2
    6. Solving Exponential Equations (I)
  7. Links to Other CCSS High School: Functions Resources
    1. Functions Resources
  8. *Additional: Links to CCSS High School: Geometry Resources
    1. Geometry Resources

1.

HSF.BF.A.1, A.1.A

  • 1. Relating SLOPE and Y-INTERCEPT to the REAL WORLD
  • 2. Writing the Equation of a Line (I-VA)
  • 3. Quiz: Modeling with Linear Functions
  • 4. Writing the Equation of a Line Given a Slope & Point (V1)
  • 5. Composition of Functions: Algebraic (Quiz)
  • 6. Writing Linear Equations Given Slope & Point (V2)
  • 7. Writing Linear Equations Given 2 Points (y-int = integer)
  • 8. Writing Linear Equations Given 2 Points (y-int not necessarily an integer)
  • 9. Quiz: Application Problems - Writing Linear Equations Given 2 Points
  • 10. Writing the Equation of a Line Given Both Intercepts
  • 11. Writing Equations of Parallel and Perpendicular Lines
  • 12. Equation of a Line: Dynamic Illustrator
  • 13. Half-Life Function
  • 14. Animation 159
  • 15. Quiz: Writing Exponential Growth & Decay Functions
  • 16. Box with Open Top

1.1.

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

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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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2.

HSF.BF.A.1.B, A.1.C

  • 1. Relating SLOPE and Y-INTERCEPT to the REAL WORLD
  • 2. Quiz: Modeling with Linear Functions
  • 3. Application Problems: Solving Linear Equations (1)
  • 4. Perimeter of a Rectangle: Solving Linear Equations
  • 5. Application Problems: Solving Linear Equations (3)
  • 6. Friends and Money: Solving Linear Equations
  • 7. Application Problems: Solving Linear Equations (5)
  • 8. Function Composition: Dynamic Illustrator (1)
  • 9. Function Composition: Dynamic Illustrator (2)
  • 10. Animation 157
  • 11. Composition of Functions: Algebraic (Quiz)
  • 12. Quiz: Composition of Functions (Graph & Table)
  • 13. Composition of Functions: Graphical (Quiz) - V1

2.1.

– 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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3.

HSF.BF.A.2

  • 1. AQR Section 21: Arithmetic or Geometric?

3.1.

AQR Section 21: Arithmetic or Geometric?

Is the sequence an [b]arithmetic sequence[/b] or a [b]geometric sequence[/b]?[br]Classify the sequence correctly.[br]You will then be prompted for the common difference or common ratio.
– Steve Phelps

4.

HSF.BF.B.3

  • 1. Function Transformations
  • 2. Transformations of Graphs (a, h, k)
  • 3. What Makes a Function Even?
  • 4. Animation 143
  • 5. What Makes a Function Odd?
  • 6. Animation 144
  • 7. Odd Functions (Another Look)
  • 8. Odd Functions: Another Look (Take 2)!

4.1.

Function Transformations

[left][color=#000000]This applet accompanies the [/color][i][color=#1e84cc][b]Transformations of Functions[/b][/color][/i][color=#000000] packet you received at the beginning of class. [/color][/left]
– Tim Brzezinski

4.2.

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4.3.

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4.4.

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4.5.

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4.6.

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4.7.

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4.8.

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5.

HSF.BF.B.4, 4.A, 4.B, 4.C, 4.D

  • 1. Inverse Relations: Graphs
  • 2. Writing Inverse Functions: Quiz (1)
  • 3. Writing Inverse Functions: Quiz (2)
  • 4. Writing Inverse Functions: Quiz (3)
  • 5. Graphing Inverse Functions: Quiz (1)

5.1.

Inverse Relations: Graphs

[color=#000000]Recall that, for any relation, the graph of this relation's inverse can be formed by reflecting the graph of this relation about the line y = x. [br][br]Recall that all functions are relations, but not all relations are functions. [br]Again, what causes a relation to be a function? Explain. [br][br]In the applet below, you can input any function [i]f[/i] and restrict its natural domain, if you choose, to input (x) values between -10 and 10. You also have the option to graph the function over its natural domain. [br][br]Interact with this applet for a few minutes, then complete the activity questions that follow. [/color]
[color=#000000][b]Directions: [/b][br][br]1) Choose the [b]"Default to Natural Domain of f"[/b] option. [br]2) Enter in the [/color][color=#980000][b]original function[/b][/color][math]f\left(x\right)=0.2x^2[/math][color=#000000]. [br]3) Choose [/color][color=#38761d][b]"Show Inverse Relation"[/b]. [/color][br][color=#000000]4) Is the [/color][color=#38761d][b]graph of this inverse relation[/b][/color][color=#000000] the graph of a function? Explain why or why not. [br]5) If your answer to (4) above was "no", uncheck the [b]"Default to Natural Domain of f"[/b] checkbox. [br]6) Now, can you come up with a set of Xmin and Xmax values so that the function shown has an inverse [br] that is a function? Explain. [br][br]At any point in this investigation, do the following:[br][br]Use the [b]Point On Object[/b] tool to plot a point on the original function.[br]Then, use the [b]Reflect About Line[/b] tool to reflect this point about the line y = x. [br]What do you notice about the coordinates of this point's reflection? Where does this point lie? [br][br]Repeat steps (1) - (6) again, this time for different functions [i]f[/i] provided to you by your instructor. [/color]
– Tim Brzezinski

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5.3.

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5.4.

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5.5.

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6.

HSF.BF.B.5

  • 1. Logarithmic Action!
  • 2. Logarithmic Action (2)!
  • 3. Logarithmic Action (3)!
  • 4. Logarithmic Action (4)!
  • 5. Logarithmic Action (4)! V2
  • 6. Solving Exponential Equations (I)

6.1.

Logarithmic Action!

Quick (Silent) Demo
– Tim Brzezinski

6.2.

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6.3.

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6.4.

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6.5.

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6.6.

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7.

Links to Other CCSS High School: Functions Resources

  • 1. Functions Resources

7.1.

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

8.

*Additional: Links to CCSS High School: Geometry Resources

  • 1. Geometry Resources

8.1.

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