1140 L20 - x y 2 1 0 1 2 3 x 2 1 0 1 2 3 y

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Lecture 20: Section 3.1 Exponential Functions Def. An exponential function with base a is a function of the form f ( x ) = a x where x is a real number, a > 0 and a 6 = 1. ex. Let f ( x ) = 4 x . Find the following: 1) f ( ± 2) 2) f (0) 3) f ± 3 2 ² The domain of f ( x ) = a x :
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Graphs of Exponential Functions ex. f ( x ) = 2 x a = 2 > 1 -2 -1 0 1 2 3 x y ex. g ( x ) = ± 1 2 ² x a = 1 2 < 1 -2 -1 0 1 2 3 x y
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NOTE: The graph of g ( x ) is the re±ection of f across the y ± axis since g ( x ) = ± 1 2 ² x = 2 ± x = f ( ± x ) NOTE: The graph of f ( x ) = a x contains these points (0 ; 1), (1 ; a ) and (1 ; 1 =a ). NOTE: Be sure to see the di²erence between the power function f ( x ) = x 4 and the exponential function f ( x ) = 4 x
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Properties of Exponential Functions f ( x ) = a x ; a > 1 f ( x ) = a x ; 0 < a < 1 (or f ( x ) = a ± x ; a > 1) 1. Domain: 1. Domain: 2. Range: 2. Range: 3. Intercept(s): 3. Intercept(s): 4. Asymptote: 4. Asymptote: 5. f ( x ) is 5. f ( x ) is and one-to-one and one-to-one
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Using Translations to Graph Graph each function and ±nd the domain, range and asymptote of the function: ex. f ( x ) = ( 4 3 ) ± x ± 1 ex. f ( x ) = ± 3 x ± 2
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1140 L20 - x y 2 1 0 1 2 3 x 2 1 0 1 2 3 y

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