A piecewise-defined function is one which is defined not by a single equation, but by two or more. Each equation is valid for some interval .
Consider the function defined as follows.
The function in this example is piecewise-linear, because each of the three parts of the graph is a line.
Piecewise-defined functions can also have discontinuities ("jumps"). The function in the example below has discontinuities at and .
Graph the function defined as shown.
Note that we use small white circles in the graph to indicate that the endpoint of a curve is not included in the graph, and solid dots to indicate endpoints that are included.
Graph the function defined below.
Negative values of and are not included in the domain because the first function, , is undefined for those values. The value is not included in the domain because the second function is not defined for that value (it has a vertical asymptote there). Therefore the domain of this function is . This can be represented using interval notation as .