Piecewise Functions

A piecewise function is one that when graphed, shows up in pieces. These functions usually have more than one function within them, consisting of two or more equations with restrictions on the size of x. For example, a piecewise function might say f(x)={x^2 if x<4; 5 if x=4; 8-x if x>4. In this example, there are essentially three mini functions that make up the function as a whole. You would use the function that covers the number you are plugging in. If one were to use f(6) in the above function, they would have to use 8-x because >4. In a piecewise function, there are always holes in the graph due to the multiple functions within it.