Monday, October 4, 2010

Chapter P - Graphing Functions

In this post I shall demonstrate how to do transformations.

1. The function I used in this graph is y=x^3.

2. I graphed this function in black at the origin.

3. Now I did a vertical translation in red and moved up by five in the y-axis. Up means add and down means subtract in the y-axis. So I have to add by 5, y=x^3+5

4. Then I did a horizontal translation in blue and moved right by 5 in the x-axis. Moving left is adding and moving right is subtracting in the x-axis. So I subtracted x by 5, y=(x-5)^3

5. In green, I did both a horizontal and vertical translation. So I moved up 5 and right 5, y=(x-5)^3+5

6. In purple, I did a reflection by adding a negative sign to the x. This flips the shape upside down,  some shapes look the same even after being reflected.

7. Finally, in black I did a reflection, vertical, and horizontal translation. I moved the shape down 5 and right 5 then flipped the image. So the equation is y=(-x-5)^3-5

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