Tutorial to explore and understand what is a periodicfunction. Before you start the tutorial, let us review the definition of a periodic function.

A function f is periodic with period P if

f(x) = f(x + P) , P is a real number.

The graph of a periodic function repeats itself indefinitely. If f is known over one period, it is known everywhere since the graph repeats itself.

Interactive Tutorial

1 - click on the button above "click here to start" and MAXIMIZE the window obtained.

2 - Use the top slider (Change shape) to change the shape of the graph of function f.

3 - Use the middle slider (Change period) to change the period of function f.

4 - Use the bottom slider( shift ), start from the left when P = 0 and change P slowly shifting the graph of f. When the graph of f in blue ( f(x) ) and the graph in red ( f(x + P) ) are identical ( superimposed ), the value of P displayed (as a multiple of Pi) is an approximation to the period of the graph of f.

5 - Change the shape and period and repeat the above exploration.