What is a piecewise function?

A function composed of two or more separate functions or pieces, each with its own specific domain, that combine to define the overall function

The domain of an absolute value function y = |f(x)| is the same as the domain of the function y = f(x).

The range of an absolute value function y = |f(x)| depends on the range of the function y = f(x). For the absolute value of a linear or quadratic function, the range will generally, but not always, be {y | y ≥ 0, y ∈ R}.