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Stitz-Zeager_College_Algebra_e-book

Use an appropriate change of base formula to convert

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Unformatted text preview: (x). • The domain of f is (0, ∞) and the range of f is (−∞, ∞). • (1, 0) is on the graph of f and x = 0 is a vertical asymptote of the graph of f . • f is one-to-one, continuous and smooth • ba = c if and only if logb (c) = a. That is, logb (c) is the exponent you put on b to obtain c. • logb (bx ) = x for all x and blogb (x) = x for all x > 0 • If b > 1: • If 0 < b < 1: – f is always increasing – f is always decreasing 0+ , – As x → 0+ , f (x) → ∞ – As x → f (x) → −∞ – As x → ∞, f (x) → ∞ – As x → ∞, f (x) → −∞ – The graph of f resembles: – The graph of f resembles: y = logb (x), b > 1 y = logb (x), 0 < b < 1 336 Exponential and Logarithmic Functions As we have mentioned, Theorem 6.2 is a consequence of Theorems 5.2 and 5.3. However, it is worth the reader’s time to understand Theorem 6.2 from an exponential perspective. For instance, we know that the domain of g (x) = log2 (x) is (0, ∞). Why? Because the range of f (x) = 2x is (0, ∞)....
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