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Unformatted text preview: Final E xanl N ame            Math 194 I nstructor            Show your work. Write down your calculations, even if you
use your calculator. T here a re 10 p roblems on 8 pages, including
t his p age. E ach n umbered problem is w orth 10 p oints. Question Possible Score
1 10 2 10 3 10 4 10 5 10 6 10 7 10 8 10 9 10 10 10 T otal 100 1. F ind t he domain of each function. x 4
a) g(x) = 
x b) f (x) = x2 I a. vx2x 2 3
+
 _ :Lb. _ 2. Let h (x) = 2 x 2  3x + 4. F ind t he average r ate of change of
g(x) from x = 2 t o x = 4.
2. _ 3. For each p art give your answer as a function f (x) = rHX + b. a) F ind a n e quation of t he l inear function t hat h as t he values
f(2) = 3 a nd f (  4) = 6.
3a. b) F ind a n e quation o f t he l inear function whose g raph is
t he line containing t he p oint (2,  2) p erpendicular to t he line
1
y = 3x + 5.
3b. _ _ 4. Consider t he f unction whose g raph is shown below. Give t he a pproximate i nterval(s) u pon which
p roperty. Circle your answers. a) f is increasing. b) f is decreasing. c) f is concave up. d) f is concave down. f e xhibits t he 5. W rite an equation for t he e xponential function whose g raph c ontains ( 0, D and (4,8).
5. _ 6. Solve each e quation for t. R ound to t he n earest O.OOL a) 3e 2t = Get.
6a. b) 5  In(2t  1) _ 6b. _ = 8. 7. A colony of b acteria is growing exponentially. Initially t here
a re 3000 b acteria in t he colony. After 4 hours, t here a re 9000
b acteria p resent. Assume t hat t he g rowth is continuous.
a) Give an explicit formula A(t) t hat gives t he p opulation of
t he colony after t hours.
7a. _ b) W hat will t he p opulation be after 8 hours?
7b. _ c) After how m any hours will t he p opulation be 100,000?
Round your answer t o t he n earest t enth of a n h our.
7c. _ 8. F ind a n e quation for t he f unction whose g raph is shown
below.
8. _ 5
)2' F ind two functions, f (x) a nd g(x), s uch
2x
t hat h(x) = g (f(x)) = (g 0 f )(x) a nd n either f (x) n or g(x) is
e qual t o x.
9. L et h(x) =( f (x) = g(x) = _ _ 10. Find a n e quation for t he p olynomial w hose g raph is shown
below. 10. _ ...
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 Spring '11
 NA
 Math, Derivative, 8 hours, Convex function, 4 hours, G raph

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