Continuity of Functions True or False

1.	Which of the following statements is true? -> A bounded function on a closed interval [a, b] must be continuous. True False
2.	Let . For which interval can we use the Boundedness Theorem to conclude that f must be bounded on that interval? -> [1, 2] True False
3.	Which of the following graphs shows a function that is both bounded and discontinuous on [a, b]? -> (a), (b), and (d) True False
4.	A continuous function on a closed interval [a, b] -> must be bounded on that interval but need not attain a maximum value on that interval. True False
5.	What is the maximum value of f(x) = sin(x) on the interval [π, 2π)? -> 0 True False
6.	A continuous function on a closed interval [a, b] -> may attain its maximum and minimum value an infinite number of times each. True False
7.	Let . For which interval(s) can we use the Extreme Value Theorem to conclude that f must attain a maximum and minimum value on that interval? -> neither [0, 1] nor [-1, 0] True False
8.	If f is continuous on [a, b] and f(b)< M < f(a) then the Intermediate Value Theorem tells us how many values of c exist in (a, b) with f(c) = M. True False
9.	Let . On which of the following intervals does the IVT guarantee the existence of a value c with f(c) = 0? -> (-3, 0) True False
10.	Which of the following pictures best illustrates the IVT? -> Picture (d) True False

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