A piecewise function is a function which is defined by different rules depending on the value of the independent variable. The following piecewise function is graphed below: y = for x≤ 0, y = x for 0 < x < 2, and y = 2 for x≥2.
A periodic function is a function with the following characteristic: f (x) = f (x + c), for all values of x, where c is some constant. This means that the values of f repeat themselves in a regular cycle. The most common periodic functions are the trigonometric functions, but others exist as well.