Going Backwards with Transformations

       A couple of days ago, we learned how to graph y= f(x) if the transformed function is given. We can determine the original function y=f(x) when the transformed function is given, by first determining what transformation(s) occurred in the function. Then, reverses the steps of transformation(s) after doing so, apply the opposite operation to the x and y point(s).

Example:

-        Given the transformed function y= 2f ½ (x+2) -1 below. What is the graph of y= f(x).

       Transformation:             To get y= f(x)                        

     - Multiply y-values by 2            - Add 1 from y-values

     - Subtract 1 from y-values         - Divide y-values by 2

     - Multiply x-values by 2           - Add 2 from x-values

     - Subtract 2 from x-values        - Divide x-values by 2

                        

     

                                                        y= 2f ½ (x+2) -1        y= f(x)

                                          (-1, 1)                      (½, 3/2)

                                                          (2, -2)                      (5/2, ­­-½)

                                                          (4,-2)                       (4, -½)

                                                          (6, 0)                       (5, ½)