• Sometimes we want to build functions that act differently for different inputs. For example, suppose a business charges $10/pizza, but only$5 for orders of six or more. How could we write a function that computes the total price based on the number of pizzas?

• In math, Piecewise Functions are functions that can behave one way for part of their Domain, and another way for a different part. In our pizza example, our function would act like costpizzas = 10 * pizzas$\displaystyle cost(pizzas) = 10 * pizzas$ for anywhere from 1-5 pizzas. But after 5, it acts like costpizzas = 5 * pizzas$\displaystyle cost(pizzas) = 5 * pizzas$.

• Piecewise functions are divided into "pieces". Each piece is divided into two parts:

1. How the function should behave

2. The domain where it behaves that way

• Our programming language can be used to write piecewise functions, too! Just as in math, each piece has two parts: fun cost​(​pizzas​): if pizzas < 6: 10 * pizzas else if pizzas >= 6: 5 * pizzas end end

Piecewise functions are powerful, and let us solve more complex problems. We can use piecewise functions in a video game to add or subtract from a character’s x-coordinate, moving it left or right depending on which key was pressed.

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