Q: How do we graph transformations that are reflections?


A: When graphing a transformations like a reflection there has to always be a line a symmetry.
a line of symmetry is a line that can make an exact replica of a figure like the butterfly below in figure one.

       Figure 1.
A reflection  is a figure that has a mirrior image.


when reflecting over x-axis or y-axis there is a rule to how to reflect them.
Reflecting over the X-axis means that the y coordinate has to be flipped.
For example: (x,y) reflected over the x-axis would be (x,-y)


To reflect over the y-axis the x coordinate would have to be flipped.
for example : (x,y) means (-x,y)


Example :
(-1,2) reflected over the x-axis would be (-1,-2) due to the fact that when reflecting over the x-axis the y coordinates changes the sign .

NOW YOU TRY IT :D

Reflect point (2,2) into the x-axis

    A.(-2,2)                   C. (2,2)                       

    B. (2,-2)                  D. (-2,-2)