4-23-10 Midterm1 soln

4-23-10 Midterm1 soln - Math 3 Midterm 1 04/23/2010...

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Unformatted text preview: Math 3 Midterm 1 04/23/2010 Instructor : Nandini Bhattaoharya Use of books, notes and graphing utilities is not permitted on this exam. Show all your work to get partial credit. You r Name: “Sig? 311?: ________________________ __ Student id# ------------------------------------------------ ~~ Your TA ------------------------------------------------ -- Max Possible Your score Problem 1: 20 Problem 2: 20 Problem 3: 15 Problem 4: 20 Problem 5: 20 Problem 6: 5 TOTAL: 1 00 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) f(x) = x2 + 6x +11 ' --- " ‘3 Ti: ‘ '-' )(i ~{ Ci. "" i x—intercept(s): ( L3 U) X 1 h 1;} ‘><‘ 13' my éw'fvmeé—ubffiXll) c ir y~intercept: { 0) “MW mmmmmmmmmm fl. H .3; é Jr VET} 0 3 it 1% Coordinates of the vertex: Axis of symmetry: «X a”: Domain and Range of f(x): Waiters ,“ til-Mitt? b) f(x) = x3 — 4ch2 ~ 5.3: x-intercept(s): L6 0 Graph: c) foe) a W —1 x~intercept(s): 4STWW :2” “‘ "’ I 3 Equation of the asymptote: :: Domain and Range of f(x): C, mam 3 fine-Wye (IMO?) I : (9*- i; (:36) 2. (20 points) Consider the function f(x) moi—3)“ w] a) Show that the function f(x) has an inverse. Hint: You can show this either algebraicaily or graphically. . SSW 5127‘?” 9%“ng fiQbW’U/i Cam/L} T 33) ~ fibrflggmm Ling. Ti?" 9 SW at (it :: [a ’ " 35.3 a) .,_ (G .3) )" > ’(m jag (J‘Wt L13” 5*- i» i no 2a) i twir- W as? “’7’” \:f“;"':“ m b) Find f 1(1) a M7 FX (3.3 )f3 ” i w») WWW b V 0) Graph both f(x) and f"(x) on the same gWgte system and d) Find the domain and range of f(x) and f""(x) . Hint: You can figure out the domain and range of f"(x) knowing that of f(x). 3. (15 points) A rancher who wishes to fence off a rectangular area finds that the fencing in the east-west direction will require extra reinforcement due to strong prevailing winds. Because of this, the cost of fencing in the east-west direction will be $12 per (linear) yard, as opposed to cost $8 per yard for fencing in the north—south direction. Find the dimensions of the largest possible rectangular area that can be fenced for $4800. a) Label all quantities in the picture below: b) Express the cost function in terms of the length and width of the rectangular area with the given constrain. Cost (2x) :13? it (“Zia-1°) ti; c) Find the dimensions of the rectangle for which the area is as large as possibie. Justify your answer with mathematics! momma“ ‘ x l. 5:? I % left WMXliWi ?Q th - > i l0 X 4~ 2‘43) Li 6 - tea 2({2flec x) “Zeuxeéx ~-\ “DH '1':- i-t??? '17:}! M M >6” t 20 ‘9 ---:«~:is*t> ~\\ 33 “f "#353me .1: 5266» we €103?) «i: H30 2 (K) WEZLX .W'” "fi:]a 4. (20 points) Assume you are given the rational function room 2 fly): (mi-Mwa x W] . Find the following: x2+JC—6 1 * (wim-.Eié"’)(><'~:ijw“‘ a) The y-intercept: ( K‘ O) J (p b) The x~intercept(s): .‘ (o (if r) r»: - E§if3>(v>2i c) The equation of the vertical asymptote(s): (X‘ its) 65:}; i Ci'i.m._m~-w i 1:: “13 J ‘ X I: d) The equatiah 0f the horizontal as. mptote (if any): W “5‘ ~ xii-W l 5 7M “ti-#5911, ig‘Q,‘.i/L,im,ctf?~fi’f X‘j f .WMMWMWW, (X r Y? ‘2‘" X‘" C0 I WW I Does the horizontal asymptote ever crosse thexgraph? ,2 p ‘ ) [fa-i" W L: r "W i inx‘ ‘ _' i it (a . a u: E (X: 912.5" Afr" £ng all intercefitema’nmamasymptotes as o a (JET: 1,. f) Sketch the graph off indicating found in a)-e). : “Maw” Mm Mammwfim W m m '/ 5. (20 points) Find equations fora linear function in the form fix.) = mx+ b satisfying the given condition: a) 1(4) = m1 and the graph off is parallel to the line 3x—8y =16. iDts: (:4 wt) grit flerefi tie gtfit‘3*””‘9 ‘15 V 3; b) The graph of 3‘ passes through the vertices of the two parabotas 1 l t. 5 yzx2+4x+1andy=~x2+9x+§~w ypw? b.1307 Gratibzf‘f \ 2 ‘2 L M_ 7‘ « Vertex 2.; ”?t “‘ " Ci - “i 5:" -~ Wm M "l t (x ( of Elf-“(2 a: FWL (1M “in (if (M - “:7 m6 .V L 1.7 , v (A t , W) ,t JV :2. f: “W 1 a _ ‘ t ( 61 i o) 3 Li m. 53 +5 :; .0 P a flu; arm, WE 95"}“6 2) W 3) 6"“) “'33 am at? (f ‘37: ‘9) é, )'ti “hii 3i;flr§-WVE“” ameafifwhiiiiiéfijéfii .1?‘ W_ wfiJwifoL 6. (5 points) Solve the following equation: ...
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4-23-10 Midterm1 soln - Math 3 Midterm 1 04/23/2010...

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