1. Transformation of Functions - Translation and stretches of functions. - Reflection in the x- and y-axis. - Rotations of functions. NOTE: You need to enable Macro’s to use the interactive aspects of the file.

2. Instructions For Use In this exercise you will get to investigate four different transformations. You will start off with translations, then stretches, reflections and finally rotations. Choose a polynomial and the function gets drawn in red. Next make a transformation and see how it effects the function. The transformed function will be in blue.

3. Translations Reflections Stretches Rotations

4. Translations y = f(x) + y = f(x + ) x 3 + x 2 + x + 12345-2-3-4-5 -2 -4 -6 -8 2 4 6 8

5. Summary Translations: f(x-c) moves the function c units to the right. f(x+c) moves the function c units to the left. f(x) + c moves the function c units parallel to the y – axis. Back

6. Stretches y = f(x) x 3 + x 2 + x + -512345-2-3-4 -2 -4 -6 -8 2 4 6 8

7. Summary Stretches: f(cx) stretches the function parallel to the x - axis by 1/c units. cf(x) stretches the function parallel to the y – axis by c units. Back

8. Reflections in x and y axis. Reflect in x axis Reflect in y axis x 3 + x 2 + x + -512345-2-3-4 -2 -4 -6 -8 2 4 6 8 Back

9. x 3 + x 2 + x + rotate by anti-clockwise around the origin. -512345-2-3-4 -2 -4 -6 -8 2 4 6 8 Back