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 ]?

-> No. This function is not bounded on [a , b ].

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 (a) nor (b)
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 the function . 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