Exam2F09_Solns

# Exam2F09_Solns - Math 105 Second Midterm Name Instructor 1...

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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 π 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 ( π ). Then the period of w ( x ) must be π . 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 h ( x )?

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