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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?
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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 for anywhere from 1-5 pizzas. But after 5, it acts like costpizzas = 5 * pizzas.
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Piecewise functions are divided into "pieces". Each piece is divided into two parts:
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How the function should behave
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The domain where it behaves that way
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Our programming language can be used to write piecewise functions, too! Just as in math, each piece has two parts:
(define (cost pizzas) (cond [(>= pizzas 6) (* 5 pizzas)])
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.
These materials were developed partly through support of the National Science Foundation,
(awards 1042210, 1535276, 1648684, and 1738598). 
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