What is the formula for graphing piecewise functions?

Piecewise function formulas for graphing have multiple definitions of the graphed function with inequalities to define where each case is true. Piecewise functions can have discontinuous segments, which are denoted on the graph as an open circle at each segment end.

To graph a piecewise function, draw each of the function's segments individually, and then erase any part of the segment that falls outside of the limits defined by the inequality. Continue to the next segment until you have drawn all segments. The function is discontinuous wherever a vertical line drawn on the graph passes through more than one point.