1105_LW4solutions_F11

1105_LW4solutions_F11 - MACllGS Lecture Worksheet 4 i. 50 (...

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Unformatted text preview: MACllGS Lecture Worksheet 4 i. 50 ( ujilfifl § Sections 4.1, 4.2, 4.4, 4.6-4.8 Fall, 2011 Decide whether each function is a polynomial. If so, state its degree and leading coefficient, a. 31) 3":4YS—V +6 Poly} cla35'3 [1:53. 6) y=3x4 Poly; okajtlsf): Q23 3 —« —- 2 :25 - J in?" b) y 3 217 r Palmdeflz.’ QT”. f) y t+7 (Fab, dfil ) 6t. Z. c) y=3f4 moi—oc‘aoly g) y d) y=(2x—1)2:(2xr|l(zx~—I) h =qu‘ahixni—l ) y {>947} 2.1mm: a) Asx—>+w,f(x)—9 “‘90 b) Asx—>—oo,f(x)—> 4‘00 c) f is an a) degree polynomial, and its leading coefficient is % 06%;! V6; . d) The local minimum value is "' ’ 0/3 , and . . 12* the local max1mum value 18 Z? . Time, e) True 01' False? Function f has no global (or absolute) extrema. ~00 t) Over what x-aXis interval(s) is f deereasing? 5 “2'3 U [2) +99 True or False? ¢+M057Ln a) Ea, ng Every 4th-degree polynomial has} 3 local extreme points. (Local extrema are sometimes called “turning points”.) b) 17f“ a“ Every 3rd-degree polynomial has at least one zero (Jr—intercept). Egan/x. Guitava (g, olel A03 r6161. {gab ave _\ f Lawn 5. image) avian in Off” 0 S" / ‘8} cl i We c'ii‘cm 5‘) 5‘6 “ll;ka jr‘eplt- Meow" Cite-053 )4 .7. 5‘ al Laxa 3 cit hcfix‘ - E 4. finite portion of the graph of polynomial f (x) is shown. Use the graph to answer all parts of this question. w 25 maximum value is 2.253 w I'D b) The global (or absolute) minimum value is 3 , a) The local minimum value is ‘“ “X3 , and the local and the global (or absolute) maximum value is 1 V?) . 5. Consider f (x) a 4x — g x3 . a) The graph of f is shown. Judging from the graph, is f even, odd, or neither? 554C! Shah!» of“? gin, gammar bay " b) Use the algebraic definitions on p.262 of the text to confirm your decision in part a). Show the work. (ax; 1" 6%)) 6. The graph of f(x) = 2253 H 4x2 H1016 +12 is shown. Write f in factored form. ad 0“; Z W :— «(Xe VT'JXXWWe m _ M) a l (v (»3)1(x~=-I)(>< ~23) 5: ZlKMbXXI-é-D 3) Answer: The'factored form of f is fix): ZOHZXWDQME 7. The factored form of polynomial f is f(x) = 0.23:2 (x + 4)(2x m1) . fl O-ZX'Lan'Z“ 45M #- At) a) f isadegree polynomial. *1“— 0:‘r‘><"”+ 1.9x m- 0,? b) Find the x-intercepts of p(x) algebraically (without the calculator). Express each answer as an ordered pair. 7..” gm x”? l X P 0.1 i 2.x” I :1: 0 $250 ?X‘:.. X230 X 2&0) (93,0) (“é/Oi c) Use a calculator to View this graph, and sketch the graph. Label the x—intercepts. Also label the local extrema with both coordinates, rounding coordinates to two decimal places, Fwy} Lice. a wimiow) weéxeq “"30 n "Then we (.1- Srnall w'mciow +0 Capbi’ure, “line. (0(1an mun “I :E-Xé Z mfég)’ «5:3 8. Write the factored form for the lowest-degree polynomial f (x) passing through (0,9) with x-intercepts at x = fi3 , 3, and 6. lion-x: CL (wthOée’a) (Ks-é) {was MM a) (raw @6091?) ammxomzxowo ~ 7e§elev chx) : t-(aeéflseltflxee?) $.W‘cz‘c Xnfiiancepll} we, “’3 J 3 J anti é) (“Mi (A. yaph Wgfiefi a main (0;?!) 9. An open box is made from a 11-inch by 8.5—inch piece of cardboard by cutting x—inch by x—inch squares from the corners and folding up the flaps. (See figure.) Volume is the product of length width and height. a) Write a formula that gives volume Vas a function of cut-size x. For what realistic domain does this construction technique make sense? ' V(x)= X IPZK 9.5%» 2.x Domain: MP Em.th b) Use the calculator to find the approximate cut size x that maximizes volume. Sketch the portion of the graph over the realistic domain, and label the local maximum point with both coordinates. Round answers to the nearest tenth, and include appropriate units. When 3:: l ““‘-\"‘?v’5 , volume is maximized at V5 :l edible» \wa; . 2x+6 x — 3 represent asymptotes, and label each asymptote with its equation. Also label the X- and y-intercepts as ordered pairs. \I'Q Whitetail W have, Knit? .3; Q X: 3 liar-is Agbwtvg, y‘g‘ Mitt? “i hijL—PoWaf flier/m. x yr‘gg a] nas$ '1}, my Fm we; vm amend» aur- w:- gfi J 5 X m w A %m$mhmmhkfl .m- 10. Consider the rational function given by f (x) a . Sketch the graph. Use dashed lines to yes; 35; x Z -r —s—7—5_:;:3 2 4 s 6 r s. 910: ’ I yr: 2». ' U) x “finite Mmpfi” y‘alth __g or: ertrle 7’: mate-:4 axew’lg OWL; as X11“? ii. 12. The surface area of a sphere is directly proportional to the square of its radius. Said another way, The surface area of a sphere is varies directly with the square of its radius. A sphere of radius 3 units will have surface area 367: square units. a) Find the constant of proportionality, and write an equation that gives surface area of a sphere, A, as a function of its radius, r. ““‘=Wflz~~.~ m' A a: K r2" g: Affirm. arm a tats)?” 3W _. .. __ _ BettaQK e» K «aw arr h) Find the surface area of a sphere of radius 6 inches, expressing the answer using appropriate units. 2) W ' .' ' , A :2 a: l SCI/mare malnog c) If radius of the sphere is tripled, surface area is multiplied by C? . Said another way, if radius of qyf‘i iwao the sphere is tripled, surface area increases by a factor of g . R am a... Pt: l’l“!’t’(3¥‘)2‘:: Hefnal‘nl“ Ci, 4th 1:: a «'3 rfi’! The intensity of Eight on an object is inversely proportional to the square of the distance from the light source to the object. At a distance of 6 meters from a particular light, the intensity of the light is 50 watts. _ a) Find the constant of proportionality, and write an equation that gives intensity, I, as a function of the x, the distance from the object to this light source. 1:: KXWZ" or” Ian»: K$50~3éfizl900 xi 5"" "i ii? - w are. kl equation: “- w 0 ‘ 2(1“ 30-": ~ 3t, b) Find the intensity at a distance of 10 meters. Answer: W ck t?) 00 7 pg (3:; j: : WW?“ WMWW” i 8 medic: l0 ' too 13. The properties of exponents and radicals are presented on p.350 and reviewed again on p.357. Use these properties to evaluate each expression: a) 49% :3 £th ‘ b) (—64% “fin-(pa 0) 10,000” :2: 5‘ mood- .7 .. (awmm 7:; is . it; at? ' I 13. a) Sketch the graphs of y 2 xé and y = 1% .9 Range [.0 1 + (19) Range @499 ~%~- (:43 z b) For integer n 2 2 , the function y = 35% is a root function. For 11 even, the domain is M and the range is I For 7? odd, the domain is M and the range is (We 0'4) -{~ 00 I 14. The graph shows a power function of the form y = kt." where p is a non—zero integer and k is a non—zero constant. Tme or false? a) M k is positive. 13) i: is e p is positive. 6) T‘l‘ ULE This is an even function. ywmfle 53vneflé’i‘f‘); t) False The domain is (—00,-1-00). Mwfi be, m K xhej even (“'ng «QWWD T: {:7 pee»: V e 15. Suppose y is inversely proportionai to the cube of x, and y = 6 when x : m1. at M «mo-w s a) Write an equation that expresses y as a function of x. Mgmiw wer- 7:: w W; fi '5 _ MK )4 a: “'5 . WK his... 7 Q (0 G“); 2. b) Findywhenx=3. Answer: y: '" gas-"n 3% 2.7M ‘7 0) Sketch the graph, making sure your artwork shows the asymptotic behavior of the graph. VIZ wwwggmm w d) Finish each statement: i) The domain of this function is (“00; O) U (0 (Tm). ii) The range of this function is (’00, 02 U ( 0 +410). iii) Asx—>+oo,yh+ O . iv) As x ——> —oo , y —> O V) This is an (even or odd) function because it has (y-axis or origin) 0 M a} )5, symmetry. ...
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1105_LW4solutions_F11 - MACllGS Lecture Worksheet 4 i. 50 (...

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