solution4B - NOTE: Be sure to bubble the answers to...

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Unformatted text preview: NOTE: Be sure to bubble the answers to questions 1 through 20 on your scantron. ' ® I Part I: points each In problems 1 through 5 indicate-whether each of the following statements is true or false. ' ~ 1. If f and g areany two functions then f o g : g o f laul'Tme all” ‘pg— XL ’ 37““; ' a " False - the) (x? = Wm) = (“03' r and“ *‘f . (3%?) (x) r egg—(all ‘ ’5‘" Kg“ _ “4*”; 2. The two functions f 2 if}; and 9(55) 2 1 have the same graph. ) True -_ p m 53‘“ giggfi $% 1“?! ' 3.‘ The polynomial function f =' 3(3: ¥ 3)2(:E +73)? has a zero of mul- " tiplicity 3. ' ( True u False 4. The polynomial function f I 3:23 — 51:21 + 13:32. I— 1 has at most 22 turning points. - '5.“Theipr<’rlrabo1awith the edfiafiéfiiflx) = —5(92 +2)2 + 3 has Vertex (—2, 3-). ' ' ' 6. On Which open interval is the function f = 45(m + 2)2'+ 3 increas— ing? ' - ’77 The average rate of change of f z 2 — x2 on the interval [1, 3] is a.1 flapfll) g (gel-42.31}; m? we: b. —1 ‘3 w! 2“ w .1. '04. 7 - ,5 «a ' “3:: ‘5’“ “‘9 8. 'Whioh' of the following functions has the same end'behavior as y: 11:3 - and crosses the x—axis at the origin? 3;; : 39(3 +_:c)(3 — m) b. f($) : 5132(23 + 3) - fix) : m + 3)(9: — 3) (:1. fix) 2 502(3 41-) 9. The function f = Jig) has dzfim‘ WMW1$£RJ¢§F } 1” (Glamoméamta‘m; a. horizontal asymptote y = 0 horizontal asymptote 2 1 c. ho'rizontal asymptote y = mg— g, a: -;: '1' (:1. no horizontal asymptote {is m m. C ("3 .p r»: (e-znlmafiw a“; fi Part II: 3 points each 11. Which of the following statements is / are true? , A. The graph of 'a rational function can cross its vertical asymptote. @Em B. The graph of a rational function can cross its horizontal asymptote. 7 I .C. if the function f has an inVerse and f(1) = 7 then f(f_1(7)) = 1. mm - - -' . WM) 12-“? _ b. Alonly ' I - @B only I d. C only e. B and C only 12. The inverse function of f is V l"- $5 “Eygwjy a X. 14. Which of the following functions is/are one—to-one? A.y::c3—a: B.y=lia:| (lysi- a. none of' these b. Aonly _ I _ . “M W " c. AandConly I d. and only only ~ X'HK sawed) _ :15. The vertex of the oarabola I 3562 -l- 53L" + 9 is. Erma?) ' ' '7 :3: ;mg b..(1,6) _ _ A Ea I 2’3- ' l ‘ . . (Co (—1,?) t : “MM «a QM) s magmas ' _1,6_) - _ 3mg «5., a} 3,0) ' ' . < 16} What is true about the function f '2 1 .— im—i— a. It has a local minimum eat-(2,1). ' I 7 ‘ 1. (i {3&9 ' ' - ' i a my ' . b.. It has a local minimum at'(~—_-2,l). ’ _- ' " ' ' . It has a local maximum at (2, 1). It has a local maximum at (—2: 1); . 'None of the above. 17. The demand function for a certain product is given by p(x_) : 200—4m Where p is theprice in Dollars and a: is thenumber ofproducts sold. What is the maximum revenue? a. $0 assesses». 5%;le 9‘4 Fix) #96 {253539999} br $25 _ “3-5” “if-£1 win» Elm K _ $50 ' lam warféfiifi ; 3.! g: m'_ fimrggggfi g $2500 g’é. El} - MW} WE? : r i E? . t I' . = arise ; amt: 18. The following table defines two functions f and-g on the domain {1, 2, 3,4, 5}: " - | l -1 - Evaluate coma—(foam)! = am) - ram) 31—27 . *«QCH-fwc‘ff) —11 a a' «i 3’ c.0, '- - _ = ,5 d.1 e. 2 ' _ 19.r__1f f(:r) I 3:2 + 1 and '(f o domain, r 72 Q a. is 335/2 + 331/2 and has domain [0, 00) kg PM?) '13. is Vang + 1 and'ha's domain (:00, oo) ' =. W 2 +4 (3. is V5132 + 1 and has domain [0, 00) I 7:» ix} + f d. is m +1 and has domain (—00, oo)_ 7:,- x a. g" 7 (a; ' a 3:an _. is 36 + 1 and has domain [0’ I 20. (Banus!) The graph of a function f lies in entirely-in the second quadrant. If f has an- inVerse function then the graph of f ‘1 . . . a. lies entireiy in the first quadrant b. lies entirely in the secondiquadrant c.' lies entirely in the third quadrant " lies entirely in the fourth quadrant xsf’fyi . lies partiy in the first and partly in the fourth quadrant. MAC 1140, Test 4 B, Part III Summer 2007 SectiOn number: I 7 Name: ' UF ID: Signaturer _ SHOW ALL WORK TO RECEIVE FULL CREDIT! 1. A farmer has a total of 160 meters of fencing. He I §"'"”“)'g"*”“' ' wants to enclose a rectangular region along a building g X , I wall and also he wantsto subdivide the region into three EWMWWW' ' smaller equal rectangular regions by placing two fences ygnmmfimm parallel‘to one of the sides. He does not need any fencing IE" Illllllf along the wall. IIlllIlIIIllllilllil a) Find an equation that eXpresses the total-area A of the region as a func- tion of the length a: (the side perpendiwlar to the wall) alone. gr fincfi. I : +— 9.): we géa :2; a» [£0 ,yx Volta... : x3, x: is fféQr-Vx) ' f: —‘f)<'."‘—+ £60K Am)=.‘.r:.‘fz<.5i.f€=.<?.?i~.p.. b) What value of a: maximizes the total area and what is this maximum total area? ‘ ' . «if—t) “a (Rik) _ I . k 1. Alma arm} :1 est-Ma + Jae-an at f/SQQ +3.25% we féflfi a3: . . . . . . . . . . . .. Maximum area:....5.;é.€§.Q...fn% . . . . . . .. 7 {mi g. a- m» we» 9o Emit} 2. Given the followng graph of the function y = f a) Sketchthe graph of the function y : —_2f + Make sure to clearly label at least four' points on the graph. ’ «S‘Btlp-Ji fine. um? I “ SM-flzfin A? 2, vmwhbéé'fg 5 $24}? Qvar xwmé 'xma fiflm) 2i" «2:.fl1)'«*~ “‘21! $92,. Kiri-6:3 :' vapfafl) =7— fii‘N!) :“"24(°’"} W 2"“ “a. :' w;{f'(‘u.2m+“§) 1?: “amp (.4) 3: Mia» f “'5. “fa. “‘3‘ “ fzmwsipawawwfl M’5 “‘7‘ "2" ‘3. Given the function 2 :1:4 — 4232‘. «1 X$(x%'*?}' 9.; X 2*" {Kai} gigéa) I a) What are the zeros of f? What are their multiplicities? ‘3‘9‘1" i might“ gwwfmm wwwiwimml mmami? : g ' a 1 b) Evaluate the following two functionvalues: 1-1—1): [—94 =63 - f(1)= r—w = c) On What open intervals is f positive (you may use a table or a sign - Chart here)? ' _ f is positive onzifTPé‘fi—l (.2. ($3.09}: . d) Sketch the graph of the function f. Make sure to clearly label all the points you found in a) and b). - ' - ' 4. Given the functiOn 2 . x ‘ 33—2117. ? 2((A'2w) -_ 3324-3: g a) What is the domain of 9‘? Use interval notation! x=t0,x.e%~“f' 3 (eardog‘mégo) wffiim} 3' b) Compute the following:%”(—2) '2 ng win 3343) = c) Find the following: Vertical asymptotes: ' x 15:» w; ' .l . ' . 0% -w_ .. Holes (5*;— and y—coordinate): x r: O y *-'—' mg W2; Zeros (gal—intercepts): g «s: g; . _ ‘ . l _ Horizontal asymptotes: 7 7-“ .7 x i d) Sketch a graph of g. Make sure to show the asyihptotes and to label the x—intercepts, the holes and the points you found in b). gi'”?’* g; - - ...
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This note was uploaded on 06/09/2011 for the course MAC 1140 taught by Professor Williamson during the Summer '08 term at University of Florida.

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solution4B - NOTE: Be sure to bubble the answers to...

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