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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 (Xll) xi’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'CﬁﬂmﬂHl :1 «Al (x HWHl 2 A“ In,“ ,  y H g “EU/ii VCr‘f‘éXi (4", Check your answer from above by using the vertex formula: XJZékTe E
Age—g Axis of symmtry like, var£5gc; X 1...! ‘ b) (5 points) f(x) = (x+3)(x—2)(x1) xintercept(s):
xz~3,;1,. !
yintercept: .
CaB){Ta—2)(y3~1): 5 Graph: c) (5 points) f(x) —2*+2 xintercept(s): .
' 0 :“lxwkla Elk—7 x :1 yintercept: ﬁgnzI 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: maﬁaHm! ill12.2 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. RaHcvﬁ‘am ﬂLCf355 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” itieeﬁH) tenser29 '3 “i [meH) +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% (rtw) ~23 [(65:19 (wiping
‘2 {@339 gig) “ i??m(>‘f‘f)3(x 9 1 ieﬂm “(XXpm '" £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. Tin4e Z Fﬁtfﬁt’x} ‘i/Lub LariZaniai 7
{frie— f‘Cs i" 7 ' 3:965 «if Chis: Obie)“ (xiiimi. 5. (20 points) Assume you are given the rational function
3x2 f(x)=m. Flnd the fOIIOWII‘lg: a) The yintercept: «4
(review WE] b) The xintercept(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 yintercept in context. (190% W03), (were we) «owM” j; AQQ?;LQQA g u..— y; 5696590 22’. "$5796 (X M19392} 'P’T—"Séiﬂﬂxl— 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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 Calculus, following expression, horizontal asymptote, simple logarithmic terms, Séiﬂﬂxl— mm loo

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