Unformatted text preview: MAC1105: Quiz #20 Solutions
July 30, 2010 In the top-right 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 (x-2)-9(x-2) = (x2 -9)(x-2) = (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) x-1 State the domain of g(x). (-, -3) (-3, 1) (1, ) State any vertical asymptotes. x = 1 1 1 State any holes. x = -3, -3-1 = - 1 , so the hole is at (-3, - 4 ) 4 Find the x and y intercepts. y -int: (0, -1); x-int: 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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- Summer '10
- Algebra, Mathematical analysis, Limit of a function, Left-wing politics, end behavior