# Transformational Graphing

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