functions - In this section were going to make sure that...

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In this section we’re going to make sure that you’re familiar with functions and function notation. Both will appear in almost every section in a Calculus class and so you will need to be able to deal with them. First, what exactly is a function? An equation will be a function if for any x in the domain of the equation (the domain is all the x ’s that can be plugged into the equation) the equation will yield exactly one value of y . This is usually easier to understand with an example. Example 1 Determine if each of the following are functions. (a) (b) Solution (a) This first one is a function. Given an x , there is only one way to square it and then add 1 to the result. So, no matter what value of x you put into the equation, there is only one possible value of y . (b) The only difference between this equation and the first is that we moved the exponent off the x and onto the y . This small change is all that is required, in this case, to change the equation from a function to something that isn’t a function. To see that this isn’t a function is fairly simple. Choose a value of
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This note was uploaded on 11/06/2011 for the course MATH 151 taught by Professor Sc during the Fall '08 term at Rutgers.

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functions - In this section were going to make sure that...

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