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Piecewise Linear Functions Some functions are made up of several different rules for different subsets of their domains. Such functions are often referred to as hybrid functions. A special case of hybrid function is when each rule is a linear function, in which case it is called a piecewise linear function. An example of such a function is f(x)={x-2 if x>4 {2x-6 if x£4 To draw this graph simply draw the graph of y=x-2 for x>2and y=2x-6 for x£4. Notice that because the two lines meet at the point (4,2) the resulting function is called a piecewise continuous linear function. An easy way to sketch these graphs is to sketch each straight line as though there were no restriction and then to erase those sections that are not required. To graph these functions on the TI-82 and the TI-83, type in y=(x-2)(x>4)+(2x-6)(x£4) (To find inequality symbols, type 2nd Math, then Test/Logic) Greatest Integer Function Another type of piecewise linear function is the greatest integer function or the step function. These graphs are made up of continuous horizontal line segments that resemble a stair case. Sample problem: It costs to $3.00 to send packages weighing between at least 1 lb but less than lb, $7.00 for packages weighing at least 3 lb but less than 5 lb, and $13.00 for packages weighing at least 5 lb but less than 8 1b. What is the equation for the step function to represent this information?
13.2 Functions
