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Unformatted text preview: n the graph of b x will increase as we move from left to right. Check out the
graph of 2 x above for verification of this property.
5. If b x = b y then x = y
All of these properties except the final one can be verified easily from the graphs in the first
example. We will hold off discussing the final property for a couple of sections where we will
actually be using it.
As a final topic in this section we need to discuss a special exponential function. In fact this is so
special that for many people this is THE exponential function. Here it is, f ( x ) = ex
where e = 2.718281828K . Note the difference between f ( x ) = b x and f ( x ) = e x . In the
first case b is any number that is meets the restrictions given above while e is a very specific
number. Also note that e is not a terminating decimal.
This special exponential function is very important and arises naturally in many areas. As noted
above, this function arises so often that many people will think of this function if you talk about
exponential functions...
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This note was uploaded on 06/06/2012 for the course ICT 4 taught by Professor Mrvinh during the Spring '12 term at Hanoi University of Technology.
 Spring '12
 MrVinh

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