Mapping Functions in the Real WorldDate: 20 Mar 1995 10:23:47 -0500 From: Maxine Fuentes Subject: functions Dear Sir: What is the purpose of learning to map a function? What is it used for in the real world? Thank you, Wayne Claire Elizee St. Thomas, Virgin Islands Date: 20 Mar 1995 10:35:19 -0500 From: Dr. Ken Subject: Re: functions Hello there! Well, the way I see it, learning to deal with functions is really learning a new way of thinking about the world. Learning to map a function is just one of the essential tools you need to use if you're going to deal with functions. Perhaps you've seen (in movies or whatever) business office meetings in which someone brings in a huge graph of the company's sales for the past year. Well, those big graphs are graphs of _functions_, like sales as a function of time. So the ability to read a graph and get information from it is really quite valuable. What's more, if you plan to do more math beyond the class you're taking now (which I sincerely hope you do!!!), you'll really need to know those functions cold. Here's one practical example of a famous real-world problem that uses functions: Farmer Bob wants to build a pen to keep his pigs in. He's got 16 Feet of fence, and he wants to use it to build the largest possible pen (i.e., the one with the most area). What shape should he build his pen in? Well, it turns out that the correct answer is to make it a circle. This is somewhat hard to prove (and yes, the proof involves functions!). But what if we say that the pen has to be some kind of rectangle? Then to find the best kind of rectangle, it turns out that you can look at the graph of the area function f(x) = x(8-x), and find where it hits its maximum value. Then you've got it. -Ken "Dr." Math |
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