Transformation with Function

                     Lesson 1


                                                            Problem:   Write the equation for the graph of function g(x), obtained by Shifting

                                                                                 the graph of f(x) = 3x2 three units left, stretching the graph

                                                                                 Vertically by a factor of six, reflecting that result over the x-axis,

                                                                                 and then translating the graph down three units. 


HTML INTRO                                                 


                                                            Solution     The original function, f(x) is graphed in red.

                                                            Step 1:         f(x) with three units to left a vertical stretch

                                                                                 By a factor of 6 is graphed. f(x) with the vertical

                                                                                 Stretch and the translation of 3 units to down

                                                                                 is graphed in green.                                                                                                                                                                                        


                                                            Solution     The final transformed function is represented by the equation

                                                            Step 2:         


                                                            Solution     f(x) =-6(x+3)2-3

Step 3:                                                            


                                                            Solution     A vertical stretch will change the y values. A translation to

                                                            Step 4:         the right will affect the x values.                                                            


                                                            Solution     Answer is:  -6(x+3)2-3

Step 5:   



                                                             Try two practice problems:  


                                                                                Solve the following: 


Given function f (x)= x2, sketch the graphs of and describe the transformation :f(2x)


Determine if the functions f(x) and g(x) are odd, even or neither: f(x)= x+2 and  g(x) = x+2










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