Example 5 Jane's Printing Services charges 29.95 to print 200 high-quality business cards. Each additional set of 100 cards costs 14 Express the cost, r(x) of printing x sets of 100 cards as a piecewise function. Solution The printing service charges for multiples of 100 cards only. If you think in sets of 100 copies, 200 copies represent two sets. Split the function into rules for the two different domains. r(x)= ) 29.95 29.95+14(x-2) when a is an integer and xgt 2 when is an integer and xleqslant 2 Notice the additional restriction on each domain. Notice that x must be a positive integer. These prices are for bulk orders only.

The cost of printing x sets of 100 cards can be expressed as a piecewise function as follows:<br /><br />$r(x)=\{ \begin{matrix} 29.95\\ 29.95+14(x-2)\end{matrix} $<br /><br />where x is a positive integer representing the number of sets of 100 cards.<br /><br />The first rule applies when x is less than or equal to 2, which means when the number of sets of 100 cards is less than or equal to 2. In this case, the cost is a fixed amount of $29.95.<br /><br />The second rule applies when x is greater than 2, which means when the number of sets of 100 cards is greater than 2. In this case, the cost is the fixed amount of $29.95 plus an additional $14 for each set of 100 cards beyond the first two sets.<br /><br />It is important to note that x must be a positive integer, as the prices are for bulk orders only.