Exploring Graphs of Absolute Value Functions in Sketchpad
Name: _____________________________________
Start Up Directions:
1.) Graph | Define New Coordinate System
2.) Go to the Mac HD. Open the Applications Folder. Open the Sketchpad Folder.
Open the Samples Folder. Open the Custom Tools folder. Open the Sliders File.
(This will add the sliders tool to Sketchpad). Minimize the Sliders File.
3.) Click
at the bottom of the Toolbar. Select Sliders. Select Basic Horizontal
Sliders.
4.) In the GSP document. Click and move the mouse three times to create three
sliders. Hit the esc key at the top left of the Mac to exit this mode.
5.) Click
on the Toolbar.
• Click on the second “a= ____” at the top. Choose the Label Tab. Change the
label to h. Click on the “a” that corresponds to the second slider. Change the
label to h.
• Click on the third “a= ____” at the top. Choose the Label Tab. Change the
label to k. Click on the “a” that corresponds to the third slider. Change the
label to k.
6.) Graph | Plot new Function. Click the parameters in the sketch to enter them
(a=, h = , k = ). Enter a*abs(x-h)+k.
Note: To adjust the sliders, select the green dot on the slider.
Adjust the sliders to that a = 1, h = 0 and k = 0.
Write the equation of the graph. ____________________________
(This is the parent function for the family of absolute value functions)
Fill out the table of values that corresponds with the function.
x
-2
-1
0
f(x)
1
Plot the parent function on the graph in red.
Adjust the sliders so that a = 1, h = 2, and k = 3.
Where is the vertex of the new graph? _____________________________
Write the new equation of the graph ______________________________
Describe the translation of the parent function to attain the new graph_____________
_______________________________________________________
2
Exploring Graphs of Absolute Value Functions in Sketchpad
Adjust the sliders so that a = 4, h = 2, and k = 3.
Where is the vertex of the new graph? _____________________________
Write the equation of the new graph ______________________________
Slope: ________
Describe the translation of the parent function to attain the new graph_____________
_______________________________________________________
Adjust the sliders so that a = -4, h = 2, and k = 3.
Where is the vertex of the new graph? _____________________________
Write the equation of the new graph ______________________________
Slope: ________
Describe the translation of the parent function to attain the new graph_____________
_______________________________________________________
Adjust the sliders so that a = 3, h = -4, and k = -1.
Where is the vertex of the new graph? _____________________________
Write the equation of the new graph ______________________________
Slope: ________
Describe the translation of the parent function to attain the new graph_____________
_______________________________________________________
Adjust the sliders so that a =
1
, h = -2, and k = -5.
2
Where is the vertex of the new graph? _____________________________
Write the equation of the new graph ______________________________
Slope: ________
Describe the translation of the parent function to attain the new graph_____________
_______________________________________________________
Adjust the sliders so that a =
1
− , h = -3, and k = 4.
5
Where is the vertex of the new graph? _____________________________
Write the equation of the new graph ______________________________
Slope:_________
Describe the translation of the parent function to attain the new graph_____________
_______________________________________________________
Exploring Graphs of Absolute Value Functions in Sketchpad
Select the green dot on the slider that corresponds with parameter a.
Describe the two things that happen to the graph as you change parameter a.
1.)________________________________________________________________
2.) _________________________________________________________________
What special property does the graph have when a = 0 ? _________________________
Select the green dot on the slider that corresponds with parameter h.
What happens to the graph as you change the parameter h? ______________________
_____________________________________________________________________
What special property does the graph have when h = 0? ? ______________________
_____________________________________________________________________
Select the green dot on the slider that corresponds with parameter k.
What happens to the graph as you change the parameter k? ______________________
_____________________________________________________________________
What special property does the graph have when k = 0 ? ______________________
_____________________________________________________________________
A little bit of fun……Animation:
1.)
2.)
3.)
4.)
Select the green dot on slider a.
Edit | Action Buttons | Animation
Label | Change Label to a
Click on the a animation button to animate. Click the a animation button to
stop animation.
5.) Select the Graph of the Absolute Value Function
6.) Display | Trace