Transformations on Parent Functions

Let f(x) be any parent function. g(x) is the transformed parent function with the defined parameters The vectors show how specific points on the parent function graph are transformed to construct the graph of the transformed function

How To Use: Double Click f(x) in the Algebra Window to change the parent function Change the values on the sliders to transform the parent function. g(x) will change accordingly in the algebra window!!! ARE THERE ANY GENERALIZATIONS YOU CAN MAKE ABOUT HOW EACH PARAMETER TRANSFORMS THE GRAPH OF THE PARENT FUNCTION???????