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ss_4_2 - Section 4.2 Exponential Functions An exponential...

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Section 4.2 Exponential Functions An exponential function , f , is a function of the form f ( x )= a x with a> 0 ,a 6 =1 Examples. The graphs of f ( x )=2 x and f ( x )=( 1 2 ) x are shown below. 4 8 –4 –2 2 4 f ( x )=2 x 4 8 –4 –2 2 4 f ( x )=( 1 2 ) x Note the following: The graph of y = a x , a> 1, is similar to the graph of y =2 x . The graph of y = a x ,0 <a< 1, is similar to the graph of y =( 1 2 ) x . Note the difference between exponential functions and power functions: y = a x is an exponential function y = x a is a power function Properties of exponentials ( a, b > 0): a s + t = a s a t ( a s ) t = a st ( ab ) s = a s b s a - s = 1 a s =( 1 a ) s Properties of the graph of y = a x , a> 1: 4 8 –4 –2 2 4 y = a x , a> 1 The y - intercept is at 1. y →∞ as x →∞ y 0as x →-∞ The graph is strictly increasing ( x 1 <x 2 implies a x 1 <a x 2 ) 1
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the graph is continuous and smooth (no breaks and no sharp corners)
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ss_4_2 - Section 4.2 Exponential Functions An exponential...

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