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Unformatted text preview: MAC1105: Quiz #20 Solutions
July 30, 2010 In the topright corner of a clean sheet of paper, write your name, UFID, and section number. Please use a pen with blue or black ink. When you are nished, FOLD your paper in half lengthwise and write your name on the back. 1. Let f (x) = x3  2x2  9x + 18 (a) Find all zeros and state their multiplicities. multiplicity 0. (b) Find the y intercept.
f (x) = (x3 2x2 )(9x+18) = x2 (x2)9(x2) = (x2 9)(x2) = (x + 3)(x  3)(x  2). So we have zeros at 3, 3, and 2, all with f (0) = 03  2(0)2  9(0) + 18 = 18. (c) Describe the end behavior of the function. Since this is a function with odd degree and positive leading coecient, the end behavior is downward to the left, upward to the right. (d) Sketch the graph. 2. Let g(x) = (a) (b) (c) (d) (e)
x+3 1 x+3 = = , x = 3 x2 + 2x  3 (x + 3)(x  1) x1 State the domain of g(x). (, 3) (3, 1) (1, ) State any vertical asymptotes. x = 1 1 1 State any holes. x = 3, 31 =  1 , so the hole is at (3,  4 ) 4 Find the x and y intercepts. y int: (0, 1); xint: None. State the horizontal asymptotes. HA: y = 0 (f) Sketch a graph of g(x). (Hint: Factor and reduce g(x), then sketch the result using transformations. Don't forget to plot holes if you nd any!) 1 The sketch should look like the basic function f (x) = x , but shifted 1 to the right by 1, and with an open dot at (3,  4 ). 1 ...
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This note was uploaded on 06/07/2011 for the course MAC 1105 taught by Professor Picklesimer during the Summer '10 term at University of Florida.
 Summer '10
 Picklesimer
 Algebra

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