6.3 Exponential Functions

6.3 Exponential Functions - Sullivan, 8th ed....

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Sullivan, 8 th ed. MAC1140/MAC1147 6-3: Exponential Functions Exponential function is a function in the form f(x) = a x where a is a positive real number and a 1. The domain of f is the set of all real numbers. The laws of exponents for real (irrational) exponents are the same as those for integer and rational exponents. Irrational exponents are truncated to a finite number of digits, so that a r a x . The number e is the number that 1 1 + F H G I K J n n approaches as n →∞ . For an exponential function f(x) = a x , a > 0, a ≠ 1, if x is a real number, then ( 29 ( 29 f x a f x + = 1 , the base. f(x) = a x Range x-intercept y-intercept Horizontal asymptote Charac- teristic Passes through a > 1 [0, ) None (0, 1) x-axis as x - Increasing, one-to-one (0, 1) (1, a) 0 < a < 1 [0, ) None (0, 1) x-axis as x →∞ Decreasing one-to-one (0, 1) (1, a) Approximate to three decimal places: 1. 3
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This note was uploaded on 01/04/2012 for the course MAC 1147 taught by Professor Staff during the Fall '08 term at Miami Dade College, Miami.

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6.3 Exponential Functions - Sullivan, 8th ed....

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