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Implied in our discussion of functions is the concept that a function may be continuous or discontinuous throughout its domain. Recall that in this function, f(x) = 1/(x+2), a gap in the graph occurred at x = –2. This restriction in the function’s domain was due to the fact division by zero is undefined mathematically. In essence, the laws of mathematics mandated this restriction. However, natural restrictions on the domain and/or range are only one type of mathematical function. If we intentionally restrict these values (or alternately expand them); we can create new functions and therefore new applications to various problem situations. In this unit we will examine special functions whereby restrictions on their domains and ranges lead to many real-world applications. These functions are called:

Step Functions -- Grocery Store

Piecewise Function (Reference) PDF

Floor [Greatest Integer] and Ceiling Functions (Reference) PDF

Below are additional educational resources and activities for this unit.

Piecewise Functions

Floor and Ceiling Functions