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112-unknown-07spex02 - 5.4 MATHEMATICS 112 EXAlVI TWO April...

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Unformatted text preview: 5.4 MATHEMATICS 112 EXAlVI TWO April 10th, 2007 Name: Instructor and section: . There are 8 problems on 9 pages (counting this page). . No graphing or programmable calculators, notes, or books are allowed. Scientific calculators are allowed but are not needed. . Give exact answers (fractions, square roots, etc.). Decimal approximations may not receive full credit. . You do not need to simplify your answers unless told to. Answers such as _ 32x/25 + 6 12 are okay. V IL' . Use only the scratch paper provided. Work appearing on your scratch paper will not be graded. . Show your work and make your methods clear. Unjustified answers may receive no credit. . Put your final answer in the box provided. Problem Possible Score 1 15 l. (5 points each) Simplify each of the following expressions as much as possible. (Answers on this page Will receive either full'credit or no credit.) ' f——' (a) V 28564314 + 4x°y6 = Answer: (0) (2x + 2y)(2‘z + 2‘9) 2 Answer: 2. Consider the function f (t) = t2 — 2t. (a) (5 points) Find the range of f (t) ! Answer: . , (b) (5 points) Find the domain of 72—15 Answer: . (c) (5 points) Find a function g(t) so that f(t) + g(t) = t2 + 2t + 3 for all values of t. S . A iswer: .— 3. (a) (3 points) Find the average rate of changed f (1:) =: fl on [9, 16].. Answer: I (b) (3 points) Find the average rate of change of 9(27) = $3 — x on {2, 3]. . Answer: 1 (c) (6 points) Let f(:c) = 1—734. Find f‘1(ac). Answer: 4. (a) (6 points) Let f (cc) 2 (at—1)? Suppose the graph of f (cc) (a parabola) is translated 4 units to the right and 3 units up, and then reflected about they — axis. Find the vertex of the new parabola. ' Answer: (13) (6 points) Find a quadratic polynomial whose graph passes through the origin and has vertex (2, 4). Answer: 5. (12 points) Suppose 2$+y = 15. Given this constraint, find the smallest possible value of 9:2 + 3/2. I . Answer: —\] 6. (12 points) Amber is building a rectangular pen. 'She wants to make the two sides that run in the east—west direction out of barbed Wire, which costs 3 per foot. The other two sides Will be chain—link fencing, which costs 5 per foot. Find the dimensions of the largest possible rectangular pen that can be built for 2400. Answer: ‘ { CE 2: + 3 neatly. You may lose points for indecipherable answers.) 7. (10 points) Draw a graph of y = . Specify all intercepts and .asymptotes. (Draw 8. (6 points each) Solve the following equations. (a) 3214-1 = 27% (b) $210m — 227101 = ——10z Answer: ...
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