Multiple Choice
Identify the
choice that best completes the statement or answers the question.
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1.
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What value of the constant a would make the
function f continuous on the interval 
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2.
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Given that  is continuous
at the point  ,
which statement(s) below must
be true based on the given?
a. | Only statement I. | d. | Only
statements I and II. | b. | Only statement
II. | e. | Only statements II and III. | c. | Only statement III. | f. | All statements I,
II, and III. |
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3.
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Given the graph
of f(x) shown above. Which is the only value below
listed for which f(x) is
continuous?
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4.
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Let f be a function that is continuous on the closed interval  with  and  . Which of the following
is guaranteed by the Intermediate Value Theorem (or Rolle’s Theorem)?
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5.
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Which of the following is NOT guaranteed by the Intermediate Value
Theorem?
a. | A plant starts growing on the day of spring and is 1
inch tall. The plant is 20 inches tall by after 50 more days. At some point between day 1
and day 50 the plant must have been 8 inches tall.
| b. | A bathtub is being filled and contains 2 inches in depth of water at 8:00
p.m. The bath tub continues to fill, some water is let out, and then filled some more. At 8:12
p.m. the tub contains 15 inches in depth of water. At some point between 8:00 p.m. and 8:12
p.m. the water depth must have been 10 inches.
| c. | At the opening of a store at 8:00 a.m. a cash register had $120 in it.
After a few transactions, the register had $342 in it by 10:15 a.m. At some point between 8:00 a.m.
and 10:15 a.m. the register must have had $200 in it.
| d. | At 8:20 a.m., Mr.Winking left home to drive to work and was 15.4 miles away
from work. By 8:25 a.m. the same day, Mr. Winking was still 11.5 miles away from work. At
some point between 8:20 a.m. and 8:25a.m. that day, Mr. Winking was exactly 12 miles away from
work.
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