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
Rotation simply rotates an object around a certain point.
Reflection
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.
