Transformations

Transformations alter a function while maintaining the original characteristics of that function.

A translation of a function is a shift in one or more directions. It is represented by adding or subtracting from either y or x.

Reflections are a type of transformation that move an entire curve such that its mirror image lies on the other side of the $x$ or $y$-axis.

Stretching and shrinking refer to transformations that alter how compact a function looks in the $x$ or $y$ direction.