Piecewise functions let us make functions that do anything we want! Example: A Doctor's fee is based on the length of time. Which we can write like this: You visit for 12 minutes, what is the …

The function ⁠ ⁠ is piecewise monotonic (subdomains , ⁠ ⁠) and piecewise differentiable (subdomains ⁠ ⁠, ⁠ ⁠, and ⁠ ⁠). Piecewise functions can be defined using the common functional notation, where …

A piecewise function is a function f (x) which has different definitions in different intervals of x. The graph of a piecewise function has different pieces corresponding to each of its definitions.

Jul 23, 2025 · A piecewise function is a function that is defined differently over different intervals of its domain. Instead of using a single equation for all inputs, it assigns distinct expressions to …

They are defined piece by piece, with various functions defining each interval. Piecewise functions can be split into as many pieces as necessary. Each piece behaves differently based on the …

Definition: Piecewise Function A piecewise function is a function that consists of multiple subfunctions, with each subfunction defined over an interval of the main function’s domain, …

To identify the domain and range of a piecewise function, we recall that a piecewise function is defined by different functions each with corresponding domains.

Piecewise functions are strongly tied to domain and range. The pieces are defined using functions or relations along with a specified domain (or sometimes range, like a vertical line).

Piecewise functions follow differnt rules depending on the value of x. Learn how to solve, graph, and read piecewise functions here!

Now, let’s look at a more generic situation involving piecewise-defined functions—one where the pieces are not necessarily constant. The best way to learn is by doing, so let’s start with an …