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Calculus I                                                           Quiz  #2                            February 13, 2004

Name____________________                    R.  Hammack                               Score ______
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 Every problem on this quiz involves the function f(x) = (1 + 8x)/(x^4 + 8x)

(1)   f(2) =(1 + 8 (2))/((2)^4 + 8 (2)) = 17/(16 + 16) = 17/32


(2)   Find the value(s) of x for which f(x) = 1
We need to solve
(1 + 8x)/(x^4 + 8x) = 1

1 + 8 x = x^4 + 8x
x^4 = 1
x = ± 1
Answer: 1 and -1 are the values of x for which f(x) = 1

(3)   Find the domain of the function  f.   
The only thing you have to look out for is values of x that make the denominator zero:
x^4 + 8x = 0
x(x^3 + 8) = 0
So you can see from this that x = 0 and x = -2 make the denominator zero.
Domain:  All real numbers except 0 and -2.