A piecewise function is a mathematical function that is defined by different expressions or formulas for different intervals of its input values. This means that the function can have different rules depending on the value of the variable. For example, a piecewise function might use one formula for values less than zero and another for values greater than or equal to zero. These functions are often used in real-world scenarios where a situation changes based on certain conditions. For instance, a tax rate might be a piecewise function, where different income levels are taxed at different rates. This allows for more accurate modeling of complex situations.