1. Warm Up Wednesday 1. Given this table, what is the slope? XY 14 512 -3-4

2. Transformations

3. Transformations in Nature

4. Transformations in Fiction

5. Transformations in Algebra

6. How do we Transform a Function?

7. Parent Function  Basically, parent functions are the function that you start a problem with before transforming it.

8. Translations  A Translation moves the parent function up/down or left/right.

9. Linear Transformations  If Kevin can buy a bag of popcorn at the theater for $4, what is his cost for 1, 2, 3 or more bags of popcorn? If Kevin has to buy a ticket for $6 before he can get in the theater, how much will it cost him for 1, 2, 3 or more bags of popcorn?

10. Vertical Translations If my parent function is f(x) = 4x and h(x) = f(x) + 6 what happens? Take your original equation f(x) and replace it in your h(x) equation so that you get h(x) = 4x + 6 Practice If f(x) = 8x and h(x) = f(x) + 2 what is h(x)? If g(t) = 12t and h(t) = g(t) - 9 what is h(t)? h(x) = 8x + 2 h(t) = 12t - 9

11. Horizontal Translation If my parent function is f(x) = 4x and h(x) = f(x + 6) what happens? Take your original equation f(x) and replace x with (x + 6) so that you get h(x) = 4(x + 6) = 4x + 24. Practice If f(x) = 8x and h(x) = f(x + 2) what is h(x)? If g(t) = 12t and h(t) = g(t - 3) what is h(t)? h(x) = 8(x+2) = 8x + 16 h(t) = 12(t – 3) = 12t - 36

12. Dilations A dilation makes the function either bigger or smaller. If the number is greater than 1, the function grows, if it is between 0 and 1, the function shrinks.

13. Vertical Dilation – Altering in the Y Direction h(x) = 16x f(a) = 2a

14. Horizontal Dilation – Altering in the X Direction

15. Summary