Piecewise-Defined Functions

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What is a piecewise function?

A function with multiple sub-functions, each applying to a different interval in the domain

What is the main requirement for the subdomains in a piecewise function?

They must be pairwise disjoint and cover the whole domain

How are piecewise functions typically defined using functional notation?

As an array of functions and associated subdomains

What is the distinguishing characteristic of a piecewise linear function?

It is composed of linear segments over different intervals

Why are bounded intervals required to have a finite number of subdomains in a piecewise function?

To ensure that the function is well-defined

Test your understanding of piecewise-defined functions, which are functions defined by multiple sub-functions, applying to different intervals in the domain. Explore how to express functions using piecewise definitions and understand the related notion of properties holding piecewise for a function.

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