Math FunctionLet’s Tame the BeastSo what is a math function? The answer lies here in. But then let’s take a different approach to understand it. Have you ever observed your Mom preparing toasts using a toaster? How does she do it? What are the steps involved and what are the participating elements? Now let’s have a critical look at this. Your Mom takes a slice of bread, puts it in a machine that is the toaster in this case and then takes out the freshly prepared toast. This is a very good analogy to understand the concept of functions. In this case the input is bread slice and the output is toast. The toaster is which processes the bread. That means it takes in the bread and gives out a toast. The toaster in the above example behaves like a function. Similar to the toaster, a function takes in input, processes it depending upon a predefined relation and delivers the output. The input that goes into the function belongs to the set called domain. In other words domain of a function is the set of all possible values that can be taken up as input for a particular function. So in our toaster example bread is the input. That means bread is a domain for the function toaster. We talked about the bread being the domain. Then what about the toast that comes out of the toaster? What do we call it in this discussion on math function? Range Yeah! That’s what it is known as in mathematical terms. The set of values that are formed as output of a function is called range. Thus the toast in our example is the output hence the range. Thus, if you imagine the function to be a black box, then anything that goes into it is called domain and anything that comes out of it is called range. Now let us consider the same toaster example again albeit with a slight twist. Instead of a loaf of bread let’s put in a piece of cloth. In this case do you think you will get the desired output that is a ready to eat yummy toast? No, absolutely not! All you will get is a burnt piece of cloth. So what is that went wrong in this math function example? Didn’t we use the same toaster as in the earlier example? We did use the toaster in working condition as in the previous example but then we took the cloth as input whereas it is not a valid input. That means the cloth is not a domain for the function toaster. Thus every function ahs a well defined domain. Similarly you can associate a function with a well defined range as well. Domain: Let us assume that the values x1, x2, x3,…etc are the valid inputs to a function f(x) Then the domain is nothing but the set containing x1, x2…etc {x1, x2, x3,…} Range: For every value of x the function will have a calculated value of the function for that x So for x1 the function will have a value f(x1). Like wise you will have f(x2), f(x3) and others The set {f(x1), f(x2), f(x3),…} is called as the range of the function. Hope this lesson on introduction to math function concepts was helpful. Stay tuned for more lessons on functions.
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