Piecewise functions

A piecewise function is a mathematical function defined by different expressions or rules over different parts of its domain. Think of it like a set of instructions that change depending on the input value. For example, a taxi fare might be calculated as one rate for the first mile and a different rate for each additional mile. These functions are useful for modeling situations where behavior changes under different conditions, such as taxes, shipping costs, or income brackets. They help represent real-world scenarios where a single formula isn’t sufficient to describe the entire range.