Product rule g uw g u g w in other words logb

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Unformatted text preview: h we have constructed are in order. As x → −∞ 1 Take a class in Differential Equations and you’ll see why. 330 Exponential and Logarithmic Functions and attains values like x = −100 or x = −1000, the function f (x) = 2x takes on values like 1 1 f (−100) = 2−100 = 2100 or f (−1000) = 2−1000 = 21000 . In other words, as x → −∞, 2x ≈ 1 ≈ very small (+) very big (+) So as x → −∞, 2x → 0+ . This is represented graphically using the x-axis (the line y = 0) as a horizontal asymptote. On the flip side, as x → ∞, we find f (100) = 2100 , f (1000) = 21000 , and so on, thus 2x → ∞. As a result, our graph suggests the range of f is (0, ∞). The graph of f passes the Horizontal Line Test which means f is one-to-one and hence invertible. We also note that when we ‘connected the dots in a pleasing fashion’, we have made the implicit assumption that f (x) = 2x is continuous2 and has a domain of all real numbers. In particular, we have suggested that things √ √ like 2 3 exist as real numbers. We should take a moment to discuss what something like 2 3 might mean, an...
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This note was uploaded on 05/03/2013 for the course MATH Algebra taught by Professor Wong during the Fall '13 term at Chicago Academy High School.

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