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Unformatted text preview: Math 105 Second Midterm November 16, 2009 Name: EXAM SOLUTIONS Instructor: Section: 1. Do not open this exam until you are told to do so. 2. This exam has 12 pages including this cover. There are 11 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 12 2 8 3 13 4 9 5 15 6 7 7 4 8 4 9 12 10 10 11 6 Total 100 Math 105 / Exam 2 (November 16, 2009) page 2 1 . [12 points] For each statement below, circle TRUE if the statement is always true. Otherwise, circle FALSE. Justification is not expected for these problems. a . [2 points] If f ( x ) is an odd function, then the graphs of f ( x ) and g ( x ) = f ( x ) are the same. True False b . [2 points] If h ( x ) is a function, then the range of h ( x ) is the same as the range of h (2 x ). True False c . [2 points] log( a b ) = log( a ) log( b ) True False d . [2 points] log( e 3 y ) = 3 y . True False e . [2 points] The angle determined by an arc of length 3 meters on a circle of radius 18 meters is 30 degrees. True False f . [2 points] Let w ( x ) be a periodic function. Suppose that w (0) = w ( ). Then the period of w ( x ) must be . True False Math 105 / Exam 2 (November 16, 2009) page 3 2 . [8 points] a . [6 points] x y The graph of f ( x ) In each of the following figures, the bold graph represents f ( x ) and the dashed graph rep resents a transformation of f ( x ). For each figure, circle one formula which best represents the given transformation. Justification is not expected for these problems. x y x y x y  f ( x ) + 50 f ( x ) + 80  f ( x ) 70 f ( x 12) 20 f (1 . 5 x ) 10 f (0 . 5 x ) 25 1 . 5 f ( x )  1 . 5 f ( x ) f ( 5 x ) 10 b . [2 points] Let g ( x ) be a function and h ( x ) = 45+ g ( x 913). What two transformations should we perform on the graph of g ( x ) to get the graph of...
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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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