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:
f1(x) = x² + 4x
f2(x) = 50
f3(x) = −10x + 21
Here is the corresponding graph:
