In mathematics, a piecewise-defined function (also called a piecewise function or a hybrid function) is a function which is defined by multiple sub functions, each sub function applying to a certain interval of the main function's domain (a sub-domain).
To evaluate the y value for a piecewise function, one must identify the location of x, which happens to be restricted in one of the intervals given. Once the location of the x is found, the next step is to choose f(x) or g(x) or h(x) to evaluate y. This implies that y is evaluated conditionally based on the location of x, that is, once the location of x is found, either f(x) or g(x) or h(x) is then used to find the y value.
The piecewise function is also graphed conditionally. This electronic document will dissect the idea behind piecewise functions.