September 14 - Function Transformations

We started class today with a clip from comedian Brian Regan about calling up UPS to pick up some boxes. This may or may not help you remember the definition of girth.

We worked a couple problems from Friday's homework. I hope that students see the details involved in describing the inverse of a given function, especially with regard to domain issues.

I presented one six-part question as a review of the ideas of function transformations. Here it is:

Given (4, 1) is a point on the graph of y = f(x), determine a point on each of the following graphs: (note the answers are in red...)

1. y = f(x) + 6 (graph moves up 6, so (4, 7))
   
2. y = f(x – 6) (graph moves right 6, so (10, 7))
   
3. y = f(6x) (horizontal shrink, so (2/3, 1))
   
4. y= 6f(x) (vertical stretch, so (4, 6))
   
5. y = Sqrt(f(x)) (similar to #4, only the y value is affected (and since Sqrt(1) = 1), the answer is (4, 1))
   
6. y = f(Sqrt(x)) (similar to #3, only the x value is affected, so the answer is (16, 1))
   

September 4 - Parent functions

We played a graphing game in class today. I projected the graph of a function on the board, and then groups in turn would guess what they thought the function was. The first round was pretty easy, while the second round was problematic as many students forgot about 1 / x and the greatest integer function. The third round was the challenge round as I changed the scale of the graphs but did not tell what that scale change was. We will complete the third round in class on Tuesday.

I have included the list of parent functions for which you are responsible below. I have also reminded you how the graphs shift right/left and up/down depending upon h, k in y = f(x–h) + k.