PP Section 5.1 - ExponentialFunctions Definition An...

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Exponential Functions
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An exponential function is a function of the form f x a x ( ) = where a is a positive real number ( a > 0) and a 1. The domain of f is the set of all real numbers. Definition
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Example: Find 2 1.41 On a scientific calculator: 2 y x 1.41 On a graphing calculator: 2 ^ 1.41 2 1.41 = 2.657371628. .. Using a Calculator
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Graphs of Exponential  Functions Base a > 1 Base 0 <a < 1
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1 : Summary = a , a f(x) x ) , ( -∞ = f D ) , 0 ( = f R No  x- intercept y -intercept:  (0, 1) -∞ = x y as 0 : Asymptote Increasing One-to-one
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1 0 : Summary < < = a , a f(x) x ) , ( -∞ = f D ) , 0 ( = f R No  x- intercept y -intercept:  (0, 1) = x y as 0 : Asymptote Decreasing One-to-one
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x x x - = = 2 2 1 2 1 : Note So the graphs of these two functions are the same. x x x y - = = = 2 2 1 2 1 Comment
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Example 3 3 of graph Sketch the 1 - = + x y Basic Graph To get the new graph, we need to shift the basic graph one unit to the left and 3 units down.
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PP Section 5.1 - ExponentialFunctions Definition An...

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