# Transformational Graphing

- Author:
- Heidi Horak

Use the following geogebra file: 3-2 Constant, Linear & Polynomial.ggb
Constant Function:
Constant functions are of the form
• Under the free objects select the function constantparent so that it is on, this is the thin function.
• Under the dependent objects select the function constanttransform so that it is on, this is the bold function.
o What values are present for c:________a:________h:________ and k:________
o Insert a positive value for c then insert a negative value for c, does it change anything? If you use a decimal? If so, what?
o Return c to 1, insert a positive value for a then insert a negative value for a, does it change anything? If you use a decimal? If so, what?
o Return a to 1, insert a positive value for h then insert a negative value for h, does it change anything? If so, what?
o Return h to 0, insert a positive value for k then insert a negative value for k, does it change anything? If so, what?
o Based on what you have observed choose a new values for c:________ a:________h:________ and k:________.
Predict what will happen to the graph. Were you right?
• Deselect the constantparent and constanttransform so that they are both off.
• Return c: 1, a:1, h: 0 and k: 0
Linear Function:
Linear functions (identity functions) are of the form
• Under the free objects select the function linearparent so that it is on, this is the thin function.
• Under the dependent objects select the function lineartransform so that it is on, this is the bold function.
o What values are currently present for c:________ a:________h:________ and k:________
o Insert a positive value for c then insert a negative value for c, does it change anything? If you use a decimal? If so, what?
o Return c to 1, insert a positive value for a then insert a negative value for a, does it change anything? If you use a decimal? If so, what?
o Return a to 1, insert a positive value for h then insert a negative value for h, does it change anything? If so, what?
o Return h to 0, insert a positive value for k then insert a negative value for k, does it change anything? If so, what?
o Based on what you have observed choose a new values for c:________ a:________h:________ and k:________.
Predict what will happen to the graph. Were you right?
• Deselect the identityparent and identitytransform so that they are both off.
• Return c: 1, a:1, h: 0 and k: 0
Quadratic Function:
Quadratic functions are of the form
• Under the free objects select the function quadraticparent so that it is on, this is the thin function.
• Under the dependent objects select the function quadratictransform so that it is on, this is the bold function.
o What values are currently present for c:________ a:________h:________ and k:________
o Insert a positive value for c then insert a negative value for c, does it change anything? If you use a decimal? If so, what?
o Return c to 1, insert a positive value for a then insert a negative value for a, does it change anything? If you use a decimal? If so, what?
o Return a to 1, insert a positive value for h then insert a negative value for h, does it change anything? If so, what?
o Return h to 0, insert a positive value for k then insert a negative value for k, does it change anything? If so, what?
o Based on what you have observed choose a new values for c:________ a:________h:________ and k:________.
o Predict what will happen to the graph. Were you right?
• Deselect the quadraticparent and quadratictransform so that they are both off.
• Return c: 1, a:1, h: 0 and k: 0
Cubic Functions:
Cubic functions are of the form
• Under the free objects select the function cubicparent so that it is on, this is a thin function.
• Under the dependent objects select the function cubictransform so that it is on, this is the bold function.
o What values are currently present for c:________ a:________h:________ and k:________
o Insert a positive value for c, then insert a negative value for c, does it change anything? If you use a decimal? If so, what?
o Return c to 1, insert a positive value for a then insert a negative value for a, does it change anything? If you use a decimal? If so, what?
o Return a to 1, insert a positive value for h then insert a negative value for h, does it change anything? If so, what?
o Return h to 0, insert a positive value for k then insert a negative value for k, does it change anything? If so, what?
o Based on what you have observed choose a new values for c:________ a:________h:________ and k:________.
Predict what will happen to the graph. Were you right?
• Deselect the cubicparent and cubictransform so that they are both off.
• Return c: 1, a:1, h: 0 and k: 0
Transformation Parameter Description of what happens when parameter is positive Description of what happens when parameter is negative
c Number 0<c< 1 Number c>1 Number -1<c<0 Number c< -1
a Number 0<a< 1 Number a>1 Number -1<a<0 Number a< -1
h
k