Section7_2_review

# Section7_2_review - Section 7.2 Exponential Functions and...

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Unformatted text preview: Section 7.2: Exponential Functions and Their Derivatives The exponential function is f x ( 29 = a x , where a is a positive constant. The graph of f x ( 29 = a x , for < a < 1 , is shown below and has the following characteristics: Decreasing Continuous Horizontal asymptote at the x-axis Passes through the point 0,1 ( 29 Domain: -∞ , ∞ ( 29 Range: 0, ∞ ( 29 lim x →∞ a x = lim x →-∞ a x = ∞ The graph of f x ( 29 = a x , for a = 1 , is shown here. The graph of f x ( 29 = a x , for a 1 , is shown below and has the following characteristics: Increasing Continuous Horizontal asymptote at the x-axis Passes through the point 0,1 ( 29 Domain: -∞ , ∞ ( 29 Range: 0, ∞ ( 29 lim x →∞ a x = ∞ lim x →-∞ a x = The natural exponential function is f x ( 29 = e x , where e ≈ 2.71828 K Since e is greater than 1, the graph of f x ( 29 = e x is increasing like the third set above: Increasing Continuous Horizontal asymptote at the x-axis Passes through the point 0,1 ( 29 Domain:...
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Section7_2_review - Section 7.2 Exponential Functions and...

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