Function

*f*of \(\mathbb{R}\) in \(\mathbb{R}\) whose rule is made up of several equations applied at different intervals of the domain. The parts that make up such a function can belong to different families of functions.The piecewise function is synonymous with a “hybrid function”.

### Example

A car starts and accelerates constantly for 5.35 seconds until it reaches a speed of 50 km/h, maintains this constant speed for the next 10.65 seconds and stops at a red light after braking constantly for 5 seconds.

This situation gives rise to a function that is defined by three parts: the acceleration interval [0; 5,35], the constant driving speed interval ]5,35; 16] and the braking interval ]16, 21]. The equations associated with each of these intervals are:

*f*_{1}(*x*) = *x*² + 4*x*

*f*_{2}(*x*) = 50

*f*_{3}(*x*) = −10*x* + 21

Here is the corresponding graph: