The Teaching Tutors - The Transformations of Graphs of Functions is Easy!
The graph of any function may be transformed either by shifting, stretching/compressing, or reflection.
For shifting and stretching/compressing, there are two types: horizontal and vertical.
A graph may also be reflected either over the x-axis or the y-axis.
1. Vertical transformations:
A shift may also be referred to as a translation. In order to vertically translate the graph of y f(x) by c units upward, c has to be added to the function. The function now becomes y f(x) + c.
For a downward translation of c units, the function becomes y f(x)