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))