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On the SAT math section, functions may move on the coordinate plane according to various rules. The base graph of  y = x or y = x2 starts at the origin, or (0,0).  
To make the graph: Do this:
flip upside down make it negative (y = -x2)
narrower multiply by an integer (y = 4x2)
wider multiply by a fraction (y = 1/5x2)
move up the graph add to the quadratic (y = x2+ 1)
move to the left add to the variable (y = (x+1)2)
When using a graphing calculator, it is important to not waste time figuring out the transformations that are not needed for the final answer. While transformations are good to know, with a calculator they are usually not needed on the SAT. 
There is also an algebraic transformation which uses the f(x) formula from algebra. 
Rotation simply rotates an object around a certain point. 
A reflection of an object is what would be seen if it was help up to a mirror to be viewed. The new image will be a mirror image of the original object. Objects that are symmetrical have a line of symmetry that is the line where reflection occurs. Objects that are symmetrical all the way around are said to have a point of symmetry. 

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