Fall 2010 MT 1(v2) Solutions

Fall 2010 MT 1(v2) Solutions - Math 3 Midterm 1 (version 2)...

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Unformatted text preview: Math 3 Midterm 1 (version 2) 10/22/2010 Instructor : Nandini Bhattacharya Use of books, notes and graphing utilities is not permitted on this exam. Show all your work to get partial credit. 7 Your Name: _____ __ Student id# ------------- -¥ --------------------------------- ~— Your TA ------------------- -------------------------- --_— Max Possible . Your score Problem 1: 20 Problem 2: 20 Problem 3: 15 Problem 4: 15 Problem 5: 20 Problem 6: 10 TOTAL: 100 1. (20 points) Give a decent sketch of the graph of the following functions. Please include all the information indicated under each part and don’t forget to carefully graph the functions at those points. a)(10 points) f(x) = —4x2 — 8x - : J’l (X-l-l) x-i’nterce pt(s): X:— 0 ,. X 3 '11 y—intercept: »Ll(a)2rZ‘CQ) :0 Coordinates of the vertex By completing the square: “Ll (film): -‘- Ll'Cfi-flmfl-Hl :1 «Al (x HW-Hl 2 A“ In,“ , - y H g “EU/ii VCr‘f‘éXi (-4", Check your answer from above by using the vertex formula: XJZ-ék-Te E Age—g- Axis of symmtry like, var-£5gc; X 1...! ‘ b) (5 points) f(x) = (x+3)(x—2)(x-1) x-intercept(s): xz~3,;1,. ! y-intercept: . Ca-B){Ta—2)(y3~1): 5 Graph: c) (5 points) f(x) —2*+2 x-intercept(s): . ' 0 :“lxwkla Elk—7 x :1 y-intercept: fignz-I 4—; 2.: 'Graph: _ 7 Equation of the asymptote: yZCz 2. (20 points) Consider the function f(x)= ,'/(x~2)+1 ‘ a) Find the domain and range of f(x) 47110: Jo l: mafia-Hm! ill-12.2- 0 X2. 1 ED «Do, w «R; H 2 art—:0 Rat—1,053 ' b) Show that the function f(x) has an inverse. Hint: You can show this either algebraically or graphically. W555 'ZwW'Zsen‘liai {Ina d) Graph both f(x) and f"(x) on the same coordinate system and explain how the graphs are related. Ra-Hcvfi‘am flLCf-355 YELX e) Find the domain and range of f"‘(x) . Hint: You can figure out the domain and range of f'1(x) knowing that of f(x). 3. (15 points) A projectile is thrown upward with an initial velocity of t76ft/sec. After t sec, its height h(t) above the ground is given h(t) = —16t2 +160r. a) Find the projectile’s height above the ground in 2 sec. M1) :1 nléQfiJ—léQQ): *ng +320 2354 b) Sketch the graph modeling the projectile’s height by labeling the x and y intercepts. -zgtliim :1 *léitltl‘dt? c) What is the projectile’s maximum height? What is the value oft at this height? h . a h fl Mali/mum l3 :6!" Vér‘fa. t” *flm ff/géi—I 5 kegju :: éltt’gf‘i. my (5) :1 Li go d) How many seconds after it is thrown will the projectile strike the ground? 4. (15 points) I a) Use the properties of logarithms to write the following expression as a sum or difference of simple logarithmic terms: log10 1/(x +1)(x + 2) . t h ' . , : “:- iogmifixfliixfl» 5-“— fi'li93;.g(x+iiix~m 3-” itieefi-H) tense-r29 '3 “i [me-H) +39 (“25 b) Use the properties of logarithms to write the following expression as a single term: ' iogmoc2 —16)— 3[l0g10(x + 4)+ 2Iogmx] :— lqgmixkit) a»: i L93 wee) i— (gym (xiii ”—'-‘ 1% (rt-w) ~23 [(65:19 (wiping ‘2 {@339 gig) “ i??m(>‘f‘f)3(x 9 1 ieflm “(XX-pm '" £0359 c) True or False? Justify your answer to receive partial credits: (x M“) (Mi (X if); x é i) logmlOOmZ e, {0311 [5%, ii) lnx3 =ln(3x) S c... " i FALSE, [Vt iii) 1m;4 = 4ln(x) f“ V - i We iv) The range of g(x) = lnx is the. set of all real numbers. True, , v)_ The function g(x) '= lnx is one“ to — one. Tin-4e Z Ffitffit’x} ‘i/Lub LariZaniai 7 {frie— f‘Cs i" 7 ' 3:965 «if Chis: Obie)“ (xiii-mi. 5. (20 points) Assume you are given the rational function 3x2 f(x)=m. Flnd the fOIIOWII‘lg: a) The y-intercept: «4 (review WE] b) The x-intercept(s): _ 5 #419 ‘m c c) The equation of the vertical asymptote(s): ‘ Wm d) The equation of the horizontal asymptote (if any): gameiegmal ‘ 3 gm- .fi ' - XQHVS ‘ WE e) Does the horizontal asymptote ever crosses the graph? f) Sketch the graph off indicating all interCepts and asymptotes as found in a)-e)i. 6. (10 points) In 2002, a newspaper company bought a new printing press for $60, 000. By 2007 the value of the press had depreciated to $32, 000. Find a linear function that model this depreciation and ' discuss the slope and y-intercept in context. (190% W03), (were we) «ow-M” j; AQQ?-;LQQA g u..— y; 5696590 22’. "$5796 (X M19392} 'P’T—"Séiflflx-l— mm loo “‘31 S lore: 1‘3 ralzolfitegre Ci‘m'iLz‘Teflt in“; ypfn"{‘wc€’f‘ir it”) 'Hu: CBS‘l" All yééif 36mm - .._.z.‘ '._....L.......";..'.._.'.;:._..._.._..__'.._...... “WHW‘WQLV " 'a - - ...
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Fall 2010 MT 1(v2) Solutions - Math 3 Midterm 1 (version 2)...

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