PP Section 5.2

# PP Section 5.2 - is an asymptote of the basic graph y =-1...

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The Exponential Function

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The number e is defined as the number that the expression 1 1 + n n approaches as n . In calculus, this is expressed using limit notation as e n n n = + →∞ lim 1 1 Definition
Using a Calculator e 2 718281827 . An approximate value for the number e can be obtained using a calculator. Your calculator must have a key labeled e x By letting x = 1 , one gets e is an irrational number.

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Definition function. l exponentia the called is ) ( function The x e x f = e 2 718281827 . is an irrational number.
e > 1 x e y = Summary and Characteristics ) , ( -∞ = f D ) , 0 ( = f R No  x- intercept y -intercept:  (0, 1) Increasing One-to-one -∞ = x y as 0 : Asymptote

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Example Graph f(x) = e –x  – 1 x e y = Basic Graph To get the graph of the new  function we need to reflect  the basic graph about the  y - axis and then shift the  graph one unit down.
Since y = 0

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Unformatted text preview: is an asymptote of the basic graph, y = -1 will be an asymptote of the new graph. Getting Ready to Graph ) , ( 1 1 1 : intercept-⇒-=-=-e y y ) , ( 1 1 : intercept-⇒ = ⇒-= ⇒ = ⇒ = ⇒-=---x x e e e e x x x x Graph of f(x) = e –x – 1 Asymptote: y = -1 Intercepts: (0, 0) Exponential Equations Example : Solve e 2x = e- 4 2x = - 4 x = - 2 We have two equal powers with the same base, so the exponents need to be equal. All the properties of exponents learned in the previous section apply when working with the exponential function. The Difference Quotient . Compute . ) ( Let h h)-f(a) f(a e x f x + = h e e h h)-f(a) f(a a h a-= + + ( 29 h e e h a 1-=...
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PP Section 5.2 - is an asymptote of the basic graph y =-1...

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