Piecewise-Defined Functions

In What Follows…

In lessons prior, you may have encountered functions whose graphs look broken up into pieces, such as

This contrasts with essentially all of the functions defined by algebraic rules that we’ve graphed thus far. So one has to wonder if there is a way to define functions that have these weird broken up graphs using algebraic rules. The answer is yes, but we have to cheat a little. We use multiple different function rules “at the same time,” in a sense, where the input plugged into the function determines which rule to use. Hence, these sorts of functions are piecewise defined.