Transformations on Parent Functions

A B Cron
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
To change the parent function, enter an expression in the Input box. 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??????? Thanks rbowers m444556