Absolute Value Function

Absolute Value Function

Function defined as follows : $$f : \mathbb{R}$$ →$$\mathbb{R}_{+}$$ : x ↦ | x |.

Symbol

The absolute value of a real number x is written as |x| and is read as “the absolute value of x “.

• The standard form of the relation that describes this function is f(x) = a |x – h| + k, in which the coordinates of the vertex are (h, k).
• The general form of the relation that describes this function is f(x) = a |bx + c| + d where a, b, c and d are real numbers.

Example

• The graphical representation of the absolute value function is :

• This is the graph of the function defined by the relation f(x) = 0.5 |5x + 1| − 3 :