# Affine Function

## Affine Function

Function defined by a relationship of the form f(x) = ax + b, where a and b are real numbers.

The Cartesian graph of an affine function is the translation of a line that represents a direct variation function.

### Examples

The function f : $$\mathbb{R}$$ → $$\mathbb{R}$$ : x ↦ 2x + 1 is an affine function.

The function f : $$\mathbb{R}$$ → $$\mathbb{R}$$ : x ↦ 3x also is an affine function, although it is generally called a linear function or a direct variation function. In this case, parameter b has a value of zero.