1105_T2Asolutions_F11

1105_T2Asolutions_F11 - MACIIOS Test2 (form A) Name: '...

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Unformatted text preview: MACIIOS Test2 (form A) Name: ' goiuil 0% Fall,'2011 ‘ Period: (arduous: TH 11:00 TH 12:30 TH 2:00 Calcuiator allowed. Follow round-off directions where applicable. Show work in spaces provided to earn partial credit. when X2: “‘i) _ 1. Consider the quadratic function y = 4x2 —4x + 5. N0 sketch required. assassin. i=0(il’“-ee>+5=e 3 a) Find the y-intercept and vertex, expressing both as oidEfied pairs. Aiso state the equation of the axis of symmetry for the graph. y, :mteFmPfiV Get“ )4 :2 0 WA?“ m “2%”, ) Answers: y-interccpt: ( O , 5 ) and vertex: ( V2- , Li" .) ‘ <_ 4+ ) > M.” Veri‘i taxi iine; 'i'ifiwuain variax 523% 20+) M I ‘ X: I/ I 4 our“) I {i 0 equation of mm oi symmetiyi L {MA-L C 3— ) 4 ) «3 b) Consider the quadratic equation 0 = 4x2 ~ 4x + 5 . Calculate the dici‘iminant and use it to ' til i ‘ . , 7— w: as complete this summary about 6 ype of solutions {92” me 3: (_ Li_) W LT (L96) a Q 1+ The discriminant = “= (0%, so there are 0 real solutions and 2 imaginary solutions. (0, i, or 2) (O, l, or 2) Li c) Use the quadratic formula to solve 0 :2 4x2 — 4x+ 5 , simplifying the solutions completeiy. W is j: :7. WWW,“ . .L ' «L n X 2a Answers: 2 + L and 2 xe- -<~»'+>it ,..<-4::;:<e1£§2m; at W .3 eases «:L :0 20+) a 8’ i=5- No‘ie: Mzflefi'fli 2. Consider the parabola given by y = —% (x + 3)2 + 4. 2 a) Circle the correct vertex: (3,4) (3,— 4) ' I” g b) Find the x—intercepts. Answers: | and m 7 W 3. Find the equation of the quadratic function y m f shown in the graph below. wwwmuk a; y:a(><~rh(><~® onbefittfi YiaWJXW49 mQMWe%MLum®M%%da. y=f(x) g (0210) , lo :2: a0: Hale? lo 2 o. (ammo-eh (£0) (£0) F5 2:. Ola lo 2::- So _ v 5 7 3 0., e; 2” —6 _3 1 :39 “exit WWW”? er in S%hddrd agree... yr; 2x1,” 12% +19 4. A rock thrown from the edge of an ocean-side cliff falls into the water below. The height of the rock 1‘ seconds after the moment of release is given by h(r) = —1 612 + 641* + 80 , measured in feet above the water. ’34 a) How high above the water was the rock released? L $3 O Rock is released at "lime £30. N03 '3‘: 5119(6) eé‘tla) tgbmswe“ ———feet ’2 b) How many seconds does it take for the rock to reach its maximum height? ‘ me... an .3. $2.512“... .. Max. hatjlmi‘ ocews 26f; 265mm 2” Answer: seconds all“ We verle x‘ . Z c) What is the maximum height of the rock above the water? Max he} \tt ocean 2‘ " cal “Hm: t“:- 2 get; I la ('22) gwiQS‘) *l“é,‘i{2.)+%0 Answel- Mfeet “3’ W :2) d) Given thatthis function is valid only from the moment the rock is released until the rock hits the water, what is its domain? h . a a: '5‘“ E ‘1 await" - Domam: M 93% O é; lime «alias welé he Waiter. It“ Wm?! Mévlwk' :: E) . _ ‘ Wham tegkiijmfit+ (ol‘i‘tiflgo H iwactvfilfi gfmmla “nu O a. “up (3&1? LH; a5) ' alga same, oungwer“, O . -Mwym “flit: .. £+i$0 ~ z tzwp‘flmPOS-QI'HQMQ’iiMQz ‘Mwafiwmwnwo-fl. b aMam-~- “mum, yaw!" A)"- .w \\ 5. Write the factored form for the lowesttggree polynomial f (as) (passing through (REDVith ' x-mterCeptS atx= -l ,2, and 5. I CL (X%(“lj)(x"2)6(m§ fix) 2 (10%” 'XKfl‘XKm-g) g : Q(O+D(Ow2a)(o”5‘> g : [06L 0cm 9 0“ V3“ Mum x10) R022? Answer: f(x) : W azu‘*vt3\i€vtii o _>(““ 6. Consider the rational function given by I; _ G, f (x) :2 3x—12 . Sketch the graph. Use dashed : it” —x + 6 3 2 l lines to represent asymptotes, and label each asymptote with its equation. Also label the x— and y—intercepts as ordered pairs. i... W m. .-.__ a: -3 it 7. Consider 32:43:”. "53> Y 5; a) Sketch the general shape of the graph on the axes below. Your sketch should show the asymptotic behavior of the graph. b) Finish each statement: A 2 i) The domain of this function is ixi X“?- 01 or "0010) U (Dfiw) 2 ii) The range of this function is i 3 I ‘J > o} 0"" (01+ 00) g iii) Asx~7>+oo, y—> O 0) True or False? This is an even function. g i) flue, g ii) Falls $1. This isaone-to-one function. /, f if f/‘w‘u {’6 an" 8. A piece of pipe is 16 inches long and open at both ends. Geometrically, this object is a right circular cylinder of radius r with volume V = 167513 . a) Complete this sentence. ‘ 1. Volume is Cure-(1+)? proportional to the '5 2 “41‘” av 5F W34 "MKS , and (directly! inversel ) a (rathusf square ofradiuslcube of radius) the constant of proportionality is . ' ' l b) If radius is halved, volume is multiplied by the numerical factor /éi‘" . '2. I “la \ Z I cavr‘ .iMLQ Vol ma. .... l) g wry-t" swims awe ‘3 My V“ iioTT"(2‘r M’TT’ 1,, 4.} 2,4. 0) Let V = f (r) denote the given volume function for r 2 0 , and let 1‘ = f fil (V) denote its inverse. Find this inverse function, use it to evaluate f ‘1 (647:) , and write a sentence that V w '2. interprets this answer. Answers: 1': \l Noll" Harrie Wymm 2; we ‘ _ _ W f‘1(64;z)=‘ 2 rsfgg: or“ ‘2‘? Sentence: pwiww) :3 fit" a: 2” When volume ‘15 é’t‘n‘ awhic‘moisefi/ radius, is 2.‘mc\r\es 9. Choose question A, or B. but not both. Check the box for the one you want graded. D A. If an object is dropped near Earth’s surface, falling time is directl proportional to the sgpare root 92;thbAdigs»)tinge_w mewwa “WW fallen. Ifit takes 1 second for the object to WWW,“ fall 16 feet, how long will it take for this object to fall 64 feet? D B. The intensity: of light inverselx prgportionm the square of the distance from the sourceitiitensitwflswla) watts at distance of 2 megs: find the intensity at a distance of 4 meters. K Kala?" or“: Ifirjegar 'u-pfirbmmaam ta: REM? to... lakfl #90 w, Wixem death 1‘?" Fjaimgo Answer: 3 0 watts Answer: 2m seconds 1 (30900 x 3 ($64)) 7 *10. Let f (x) = «Ix — 2 and g(x) = — . Find the formula for ( g o f) and state its domain. l (go f)(x)= Domain: ax i x i) 2”; mm. (2) +90) 11. Function f is given by the graph below. Function g is defined only for the x-values in the table below. Evaluate each expression. Some expressions may be “undefined”. _ a) [gen -‘“’53:” =‘ L33 b) (gof)(1)=j(f0)): 3( = c) (fg)(1)= mogms 2’ 3’ d) (f+g"1)(3)= to) + 3"(3) Graph of f 12. The graph of f (x) 2 at2 +1 is shown for x 2 0 . Find the inverse function f’1 Sketch its graph on the figure that shows f and label its x—intercept with both coordinates. Also state the domain and range of f "i . tat-mamas.“ Kiwm? 'miernhamflfi VMlt’tme‘E \lx fans): the»; ' Domainoff‘]: Ki 0r CHM“) Rangeoff": i 3250“; 9"” E0) +93) 13. Write True or False in each blank: szwfii m 9&5) i a For parts a)-b), let y = (1x2 + bx + 0 represent the parabola shown. HNH-Ihmm a) Tvme. c>0 b) True, b2—4ac>0 .Lihylpfi: c) M If a polynomial has high-power term —33€‘t , then as x ”’ ‘00 ’ y $@’ and W as x —> +00 , y —> a " d) hai '3' e Every filth-degree polynomial has math: 3 local extreme points, or “tumng points”. A I. ua‘i‘ mos‘f’" makes “Hm; 'ivue U mas For parts e)-g), let f (x) be the polynomial shown. 3°“) a“ “m ("2.5.3.93 6) [Sal Se f (x) is positive over [—3,—1]U[1,+oo). 6‘3)" U C f) True. f(x) is decreasing over [—2.15,0.15]. local min point g) gang f (x) is one-to-one. (ii-15.498) Mari genial ling “i‘fi‘. 5+" afiaiis . . The graph shown is a power function of the form y = kx" where p 13 a non~zero integer and k is a non-zero constant. Use this graph for parts h)-j)- . ' Looks it k3 x h) Foe 5 er: k is positive. a 3 i) Fad S E. p is positive. Y a”: K X j) “Wm—s12 isodd. $0.. ks o k) TWH e For function y = x%’ where n is a positive even integer, the domain is [0,-E-w). l) TWU» e If f(x) : «far—2 and g(x) = $ , the domain of (f+g)(x) is [2,+oo). ...
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1105_T2Asolutions_F11 - MACIIOS Test2 (form A) Name: '...

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