In mathematics, a transformation is a function f (usually with some geometrical underpinning) that maps a set X to itself, i.e. f : X → X. In other areas of mathematics, a transformation may simply refer to any function, regardless of domain and codomain. For this wider sense of the term, see function (mathematics).
How do transformations affect functions?
A function can be compressed or stretched vertically by multiplying the output by a constant. A function can be compressed or stretched horizontally by multiplying the input by a constant. The order in which different transformations are applied does affect the final function.
How do you know if a transformation is a function?
The function translation / transformation rules:
- f (x) + b shifts the function b units upward.
- f (x) – b shifts the function b units downward.
- f (x + b) shifts the function b units to the left.
- f (x – b) shifts the function b units to the right.
- –f (x) reflects the function in the x-axis (that is, upside-down).
