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Unformatted text preview: Math 3 Midterm 1 (version 2) April 29, 2011
instructor : Nandini Bhattacharya Use of books, notes and graphing utilities is not permitted on this
exam. Show all your work to get partial credit. Your Name:  \3
Student id#  u u u _ — — — q n u.— _ Your TA and section time:   Max Possible Your score Problem 1: 10 Problem 2: 15 Problem 3: 10 Problem 4: 20 Problem 5: 15 Problem 6: 15 Problem 7: 15 TOTAL: 1 00 1. (10 points) Give a decent sketch of the graph of the following
functions. Please include all the information indicated and don’t
forget to carefully graph the functions at those points. f(x)=—x2w2x+3 "W; I K (mﬂxﬁ “Muweﬁ ’2 13 2“ Coordinates of the vertex yamQ a By completing the square: 2. (15 points) a) Let f(x)=\/x2+3x—4. Find the domain of f(x). "yik’éx—«iﬁ :3 g I' w“ ‘“ ’ ’ —« J J. '= ‘ z W
“E” “"" ' T44?» A I
H_._M “Xi”??? Wm§ ﬂea—.1 4?.
b) Let f(x)=x2—x and g(x)=1—2x. Compute each of the following: i) (f—gxx) 3 0) Give a reason why each of the following graph can not represent a
polynomial function that has the highest term 2x5. ——“: i. ' timer{@1254}; WURJ‘E, _ 3 a
inlaid” Mtge“ alg w
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5”?“ gainfuiik! J @52/ Sb’vxﬁﬁt‘r’i’irw 3. (10 points) Find the resultant function and its graph obtained by
following the transformations applied to the graph of y=—1—,X>0 given
E x in the following order: i a) Reflected about the x—axis. “\ ’ Ml
B >6 #0 y M a—l
4. (20 points) Assume you are given the rational function
f(x)=x2+8x+7 8x2 + 8x Hint: Keep track lof your domain Find the following: a) The y—intercept. r W a, i: J... ., ' a” K ﬂ Q '1. LE? MWQE‘} XIV»,th b) The xintercept(s); % «w
“d “5‘ Q ﬂxﬁﬁ M in . N)
LE? M {I ME) (1" J c) The equation of the vertical asymptoteg) 4% J ~ d) The equation of the horizontal asymptote (if any): e) Does the horizontal asymptote ever crosses the graph? 5. (15 points) The perimeter of a rectangle is 12m. a) Draw the rectangle labeling all sides and the diagonal. M! P ___V_mm_.. it
La” 1:. E r .
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Wol— b) Write an equation that relates the two sides of the rectangle and
the diagonal Hint: The Famous Theorem! ,3; F2“ 5 ../_._
x " {a 2:. A “is {£2
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(.1. c) Find the dimensions for which the diagonal is as short as possible .. .1 1?,» ‘E p r, ‘ ' In“ 'lf‘mv'mm‘liﬁ, 'l’tm "‘fimzzrx r‘mwamvw a z. a 6. (15 points) Consider the function f(x)=e"+‘ a) Show that the function f(x) has an inverse. Hint: You can show
this eitheraigebraically or graﬁiically. Ki) {Eta/L (TRhi» {Ed/g? “ 
it V «a r iii“ 0r" EM tea: 1. i
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awﬁiwmmem—g y u ,W......___.m.m~mu—v—v WWW“ﬂ~~~m~wh_.~——..._......H____,,w._.—g
Ww_.,.._..w a" r www.mwtzw fﬁl (x)
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,2 I: ,1.‘ BC “:— {JVT m ' mar"4"“
’mJbM “FF “*— ‘Rwﬂ 0) Graph both f(x) and flea) on the same coordinate system and
explain how the graphs are related. ft“ .2
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5 2 “‘3
f, d) Find the domain and range0t f‘1(x) xiii/ht: You can figure out
the domain and range of f"(x) knowing that of f(x). “2“ w “W “i it {m} 3“ fem/Mi) neﬁ.a\%mr‘ﬂi \
i i J ,4 \ Ji— {Aé‘i / w ‘
{ﬁtmgwi ' ’ U4: (7" e53 ' I / 7 (15 points) Solve the following equations: a) loglooi2 + 36) 2 2
iii") {1o £2, “ﬁrm ‘
ﬁﬂg‘xw‘gwg /
n. {\ C) 10g6x+10g6(x+1): 0 memm,» 1. ...
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