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Unformatted text preview: Math 105 Final Exam December 17, 2010 Name: Instructor: Section: 1. Do not open this exam until you are told to do so. 2. This exam has 13 pages including this cover. There are 10 problems. Note that the problems are not of equal difficulty, so you may want to skip over and return to a problem on which you are stuck. 3. Do not separate the pages of this exam. If they do become separated, write your name on every page and point this out to your instructor when you hand in the exam. 4. Please read the instructions for each individual problem carefully. One of the skills being tested on this exam is your ability to interpret mathematical questions, so instructors will not answer questions about exam problems during the exam. 5. Show an appropriate amount of work (including appropriate explanation) for each problem, so that graders can see not only your answer but how you obtained it. Include units in your answer where that is appropriate. 6. You may use any calculator except a TI92 (or other calculator with a full alphanumeric keypad). However, you must show work for any calculation which we have learned how to do in this course. 7. If you use graphs or tables to find an answer, be sure to include an explanation and sketch of the graph, and to write out the entries of the table that you use. 8. Turn off all cell phones and pagers , and remove all headphones. Problem Points Score 1 10 2 10 3 18 4 9 5 5 6 5 7 9 8 10 9 14 10 10 Total 100 Math 105 / Final (December 17, 2010) page 2 1 . [10 points] For each statement below, circle True if the statement is always true. Otherwise, circle False . You do not have to show any work for your answers. a . [2 points] If f is an invertible function and f (5) = 2, then f 1 (5) = 1 2 . True False b . [2 points] If h is an invertible function, then the domain of h 1 is the range of h . True False c . [2 points] If a radioactive substance decays 25% every year, then its halflife is two years. True False d . [2 points] The function f ( x ) = e 2 x + 1 is a linear function. True False e . [2 points] The line y = 4 is a horizontal asymptote of the function y = f ( x ) = 3 5 x 2 + 4 x x + 2 . True False Math 105 / Final (December 17, 2010) page 3 2 . [10 points] a . [5 points] A portion of the graph of a power function q ( x ) is shown below. Find a formula for q ( x ). x (1 , 9) (3 , 1 3 ) y = q ( x ) y Answer: q ( x ) = b . [5 points] A portion of the graph of a polynomial function p ( x ) is shown below. Find a possible formula for p ( x ). 1 2 3 4 1 2 3 4 4 8 4 8 b b b y = p ( x ) x y Answer: p ( x ) = Math 105 / Final (December 17, 2010) page 4 3 . [18 points] a . [5 points] Suppose that the amount of time (in hours) that it takes to clean up the stadium after a soldout football game is inversely proportional to the square of the number of volunteers who are cleaning. It took 5 hours for 100 volunteers to clean up after a recentvolunteers who are cleaning....
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This note was uploaded on 01/28/2012 for the course MATH 105 taught by Professor Rhea during the Fall '08 term at University of Michigan.
 Fall '08
 Rhea
 Math

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