A function f(x) is a piecewise continuous function on an interval I if it is a continuous function on the whole I except finite number of points of discontinuity of the first order. The point of discontinuity of the first order is a point for which the function has the limit from the right and from the left. If on each subinterval the function is a linear function then it is a piecewise linear function. Note that the equality y = f(x) defines a function if for each x there exists not more than one y. The model demonstrates a construction technique of a piecewise linear function. The function is defined as a set of equations on different intervals. If you choose the Demonstration radio button, click the Build button and look at the building process. A blue filled point indicates a point where f(x) is specified, a point with hole indicates a pole where f(x) is unspecified. The next button produces a different example of a function and its graph. If you choose the Plot the function graph radio button, a graph of specified function will appear, but all end of linear segments (in points of discontinuity) will be filled in gray. Click on a point to change a point type. Set type for all gray points and press the check button. Choose the Find the definition domain radio button to select a function domain for the each piece based on plotted graph.
