A piecewise function is used when a situation or relationship changes depending on the input value crossing certain boundaries or intervals. Instead of having a single formula that applies to all inputs, a piecewise function uses different formulas for different parts of the input domain. This is useful when different rules apply to different ranges of values, for example:
- When a product's price changes depending on the quantity bought, such as a regular price for fewer units and a discounted price for bulk purchases.
- When tax rates change at specific income levels, where income up to a certain limit is taxed at one rate and anything above that limit at a different rate.
- In real-world scenarios where the behavior of a function varies in pieces, like shipping costs for groups of different sizes or absolute value functions.
Essentially, piecewise functions describe situations where the rule or relationship changes at specific points, providing a precise way to model changing conditions across intervals of input values.
