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Unformatted text preview: Section 7.2: Exponential Functions and Their Derivatives The exponential function is f x ( 29 = a x , where a is a positive constant. The graph of f x ( 29 = a x , for < a < 1 , is shown below and has the following characteristics: Decreasing Continuous Horizontal asymptote at the xaxis Passes through the point 0,1 ( 29 Domain:  , ( 29 Range: 0, ( 29 lim x a x = lim x  a x = The graph of f x ( 29 = a x , for a = 1 , is shown here. The graph of f x ( 29 = a x , for a 1 , is shown below and has the following characteristics: Increasing Continuous Horizontal asymptote at the xaxis Passes through the point 0,1 ( 29 Domain:  , ( 29 Range: 0, ( 29 lim x a x = lim x  a x = The natural exponential function is f x ( 29 = e x , where e 2.71828 K Since e is greater than 1, the graph of f x ( 29 = e x is increasing like the third set above: Increasing Continuous Horizontal asymptote at the xaxis Passes through the point 0,1 ( 29 Domain:...
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 Fall '07
 FAMIGLIETTI
 Math, Exponential Function, Derivative, Exponential Functions

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