Written by the Fiveable Content Team • Last updated September 2025
Verified for the 2026 exam
Verified for the 2026 exam•Written by the Fiveable Content Team • Last updated September 2025
Definition
The absolute value function is a mathematical function that gives the distance of a number from zero on the number line. It returns the positive value of any given input.
The domain of an absolute value function refers to all possible input values for which the function is defined. For example, in |x|, x can be any real number.
The range of an absolute value function refers to all possible output values that the function can produce. In |x|, the range includes all non-negative real numbers.
Piecewise Function: A piecewise function is made up of different rules or formulas applied to different parts (or pieces) of its domain. An absolute value function is often represented using piecewise notation because it has different behaviors for positive and negative inputs.