Step FunctionsThe Postage Stamp Problem: Figure 1-6p shows the graph of the greatest

Chapter 1, Problem 12

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Step FunctionsThe Postage Stamp Problem: Figure 1-6p shows the graph of the greatest integer function, f(x) = [x]. In this function, [x] is the greatest integer less than or equal to x. For instance, [3.9] = 3, [5] = 5, and [2.1] = a. Plot the greatest integer function using dot style so that points will not be connected. Most graphers use the symbol int(x) for [x]. Use a friendly x-window that has the integers as grid points. Trace to x = 2.9, x = 3, and x = 3. What do you find for the three y-values? b. In the year 2001, the postage for a first-class letter was 34 cents for weights up to one ounce and 23 cents more for each additional ounce or fraction of an ounce. Sketch the graph of this function. c. Using a transformation of the greatest integer function, write an equation for the postage as a function of the weight. Plot it on your grapher. Does the graph agree with the one you sketched in part b? d. First-class postage rates apply only until the letter reaches the weight at which the postage would exceed $3.2 What is the domain of the function in part c? 1