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March 24, 2017

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If g(x) is continuous for all real numbers and g(3) = -1, g(4) = 2, which of the following are necessarily true?
I. g(x) = 1 at least once
II. lim g(x) = g(3.5) as x aproaches 3.5.
III. lim g(x) as x approaches 3 from the left = lim g(x) as x approaches from the right

A. I only
B. II only
C. I and II only
D. I, II, and III
E. None of these.

I want to say that the answer should be D. I, II, and III since the function is continuous for all real numbers. Would this be correct?

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