To graph a piecewise function, first identify the domains of each subfunction using intervals. Then, use each function and each of their corresponding intervals to graph each piece of the piecewise function. Any points omitted by the interval are not graphed by the function, as they will typically be included in other intervals.

Firstly, identify each of the domains corresponding to the different subfunctions of the piecewise function. Then, look at the inputs and outputs of each of the functions and their corresponding intervals. Then, graph each piece of the piecewise function defined on each interval. Once all pieces have been graphed, the final piecewise graph is done.

For example, consider the piecewise function defined by p(x) = { -x if x< 0 and x if x is greater than or equal to zero. The two intervals in this example are (-infinity, 0) and 0, infinity). Graphing y=-x first on the interval (-infinity, 0) will yield the first part of the graph. Then, graph y=x on the interval [0,infinity) to get the last piece. This will also be the graph of the absolute value function; this is another way to define it. Once both pieces have been graphed, the piecewise graph is done.