## Friday, October 1, 2010

### Ch. P - Graphing Functtions

1. I started by graphing the original (parent) function of y = ³√x (cubic root of X), which is the graph (black) intersecting the origin.
2. Next, I translated the function y = ³√x, 9 units up along the y-axis to create a vertical translation of y = ³√x+9. The translation is shown in red intersecting at (0,9).
3. Then I created a horizontal translation, by moving the function 9 units to the right along the x-axis to create y = ³√(x-9). The translation is shown in blue intersecting at (9,0).
4. Then I combined both vertical and horizontal translation, I transformed the original function into y = ³√(x-9)+9, where the graph moved 9 units to the right of the x-axis then 9 units up the y-axis. The translation is shown in green marker in the first quadrant and intersecting at (9,9).
5. Then I did a reflection where I reflected the original function across the x-axis to create y = -³√x which is shown in purple intersecting at the origin.
6. Finally, I graphed a transformation by combining the vertical translation, horizontal translation and the reflection over the x-axis. I moved the original function reflected across the x-axis, translated 9 units to the right and 9 units down to make y= -³√(x-9)-9. The transformation is shown in black marker in the fourth quadrant intersecting at (9,-9).