Tuesday, September 27, 2011

CH P Graphing Function

In class, we were graphing functions of different kinds of transformations.

The picture shown to the left is the function y=x2 (squared).

1.)The original function is y=x2 which is in black.

2.)Then, up next is the transformation to vertical translation which is shifting up or down the units given. My equation is y=x2 + 3 which is shifting the y-axis up 3.

3.)The next transformation is the horizontal translation which is taking the given function and shifting it left or right by units given. My equation is y=(x-7)2 which shifted 7 units right in the x-axis. When X is subtracting a number given, then it is going to the right, but when it is adding a given number, then it goes to the left.

4.)I then combined an equation with vertical and horizontal translation. My equation i chosed was y=(x+3)2 - 2. This equation is shifted 3 unites to the left and 2 units down. To do this equation is the same as the ones above, but instead, I put both transformation together in one equation.

5.)The graph that looks upside down is the reflections. reflection is given when the given function is negative. My equation shows y= -x2. This equation is just the opposite of the original equation. They are ''reflecting", folding your paper hamburger style shows the reflection vertically.

6.) There is also an horizontal reflection, which is the having an negative X in an equation. For example, look at my original function, there is also another color outlining it which is y=(-x)2. This is the reflection horizontally, it is like folding your paper hot dog style, getting a mirror image.

7.)The last graph showed is combining both translations and reflections together. My equation shows y= -(x-4)2 - 2. This is pretty much the same as combining both the horizontal and vertical translation but yo also include the reflections together.

In conclusion, this shows the different transformation for the parent function y=x2(squared).