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mt-3sum10

# mt-3sum10 - Math 3 MIDTERM EXAM Math 3 Dr Frank Buerle UCSC...

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Math 3 MIDTERM EXAM Math 3 7/9/2010 , Dr. Frank B¨auerle, UCSC Note: Show your work. In other words, just writing the answer, even if correct, may not be sufficient for full credit. Scientific calcula- tors are allowed, but no programmable and/or graphing calculators. Your Name: Your TA’s Name: Problem 1: out of 20 Problem 2: out of 10 Problem 3: out of 10 Problem 4: out of 15 Problem 5: out of 15 Problem 6: out of 15 Problem 7: out of 15 Total: out of 100 Good luck! 1

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1. (20 points) Give a decent sketch of the graph of the following functions. Don’t forget to supply all the requested information such as intercepts, vertex, etc. (a) f ( x ) = x 4 - 1 x -intercept(s): y -intercept: (b) f ( x ) = ( x - 1)( x + 3) x -intercept(s): y -intercept: Coordinates of vertex: (c) g ( x ) = 2 x - 1 x -intercept(s): y -intercept: equation of horizontal asymptote: (d) g ( x ) = ln( x + 1) x -intercept(s): y -intercept: equation of vertical asymptote: 2
2. (10 points) Consider the function f ( x ) = ( x + 1) 5 + 1 (a) (2 points) Give the domain of f ( x ) (b) (6 points) Find the equation for f - 1 ( x ) (c) (2 points) Give the domain of f - 1 ( x ) 3

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3. (10 points) For this problem, assume that the number of fans of a certain brand of
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