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CA_GPS_25

# CA_GPS_25 - 1<< = a a x f x is a decreasing one-to-one...

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Rev. S08 http://faculty.valenciacc.edu/ashaw/ COLLEGE ALGEBRA NAME: ________________________________ GPS # 25 3.1 EXPONENTIAL FUNCTIONS I Class Time: ____________ Date: __________ Useful Guidelines: * An exponential function: x a x f = ) ( , where 0 > a and 1 ! a . The domain of f is the set of all real numbers. [Note that the base is a constant and the exponent is a variable.] ... 718281828 . 2 = e * Properties of the Exponential Function x a x f = ) ( (where 0 > a and 1 ! a ): (1) Domain: the interval ) , ( ! "! ; Range: the interval ) , 0 ( ! ; (2) x -intercepts: none; y -intercept: 1; (3) Horizontal asymptote: 0 = y as ! " x ; (4) 1 , ) ( > = a a x f x , is an increasing, one-to-one, smooth and continuous function;
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Unformatted text preview: 1 , ) ( < < = a a x f x , is a decreasing, one-to-one, smooth and continuous function; (5) The points ), , 1 ( ), 1 , ( a and ) , 1 ( 1 a ! are always on the graph of f . 1. Evaluate x x f 3 ) ( = at , 2 , 1 , , 1 , 2 ! ! = x and 3. Graph the exponential function. 2. Evaluate x x g ! " # \$ % & = 3 1 ) ( at , 2 , 1 , , 1 , 2 ! ! = x and 3. Graph the exponential function. 3. Graph each function and determine the y-intercept, domain, range, and horizontal asymptote of f . (a) 2 3 ) ( ! = ! x x f (b) x e x f = ) (...
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