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L20 - Lecture 20 Section 3.1 Exponential Functions Def An...

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Lecture 20: Section 3.1 Exponential Functions Def. An exponential function with base u1D44E is a function of the form where u1D465 is a real number, u1D44E> 0 and u1D44E = 1. ex. Let u1D453 ( u1D465 ) = 4 u1D465 . Find the following: 1) u1D453 ( 2) 2) u1D453 uni0028.alt03 3 2 uni0029.alt03 The domain of u1D453 ( u1D465 ) = u1D44E u1D465 : NOTE: Be sure to see the difference between the power function u1D453 ( u1D465 ) = u1D465 4 and the exponential function u1D453 ( u1D465 ) = 4 u1D465
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Graphs of Exponential Functions ex. u1D453 ( u1D465 ) = 2 u1D465 -2 -1 0 1 2 3 x y ex. u1D454 ( u1D465 ) = uni0028.alt03 1 2 uni0029.alt03 u1D465 -2 -1 0 1 2 3 x y NOTE: The graph of u1D454 ( u1D465 ) is the reflection of u1D453 across the u1D466 -axis since u1D454 ( u1D465 ) = uni0028.alt03 1 2 uni0029.alt03 u1D465 =
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Properties of Exponential Functions u1D453 ( u1D465 ) = u1D44E u1D465 ,u1D44E> 1 u1D453 ( u1D465 ) = u1D44E u1D465 , 0 <u1D44E< 1 (or u1D453 ( u1D465 ) = u1D44E u1D465 ,u1D44E> 1) 1. Domain: 1. Domain: 2. Range: 2. Range: 3. Intercept(s): 3. Intercept(s): 4. Asymptote: 4. Asymptote: 5. u1D453 ( u1D465 ) is 5. u1D453 ( u1D465 ) is and one-to-one and one-to-one 6. Points uni0028.alt03 1 , 1 u1D44E uni0029.alt03 , (1 ,u1D44E ) are on each graph
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