This preview shows pages 1–9. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: NOTE: Be sure to bubble the answers to questions 1 through 20 on
your scantron. ' ® I Part I: points each In problems 1 through 5 indicatewhether each of the following statements
is true or false. '
~ 1. If f and g areany two functions then f o g : g o f
laul'Tme all” ‘pg— XL ’ 37““; ' a " False  the) (x? = Wm) = (“03' r and“ *‘f . (3%?) (x) r egg—(all ‘ ’5‘" Kg“ _ “4*”;
2. The two functions f 2 if}; and 9(55) 2 1 have the same graph. ) True _ p m 53‘“ giggﬁ $% 1“?! ' 3.‘ The polynomial function f =' 3(3: ¥ 3)2(:E +73)? has a zero of mul
" tiplicity 3. ' ( True u False 4. The polynomial function f I 3:23 — 51:21 + 13:32. I— 1 has at most 22
turning points.  '5.“Theipr<’rlrabo1awith the edﬁaﬁéﬁiﬂx) = —5(92 +2)2 + 3 has Vertex
(—2, 3). ' ' ' 6. On Which open interval is the function f = 45(m + 2)2'+ 3 increas—
ing? '  ’77 The average rate of change of f z 2 — x2 on the interval [1, 3] is a.1 ﬂapﬂl) g (gel42.31}; m? we: b. —1 ‘3 w! 2“ w .1.
'04. 7  ,5 «a ' “3:: ‘5’“ “‘9 8. 'Whioh' of the following functions has the same end'behavior as y: 11:3
 and crosses the x—axis at the origin? 3;; : 39(3 +_:c)(3 — m)
b. f($) : 5132(23 + 3) 
ﬁx) : m + 3)(9: — 3)
(:1. ﬁx) 2 502(3 41) 9. The function f = Jig) has dzﬁm‘ WMW1$£RJ¢§F }
1” (Glamoméamta‘m; a. horizontal asymptote y = 0 horizontal asymptote 2 1 c. ho'rizontal asymptote y = mg— g, a: ;: '1' (:1. no horizontal asymptote {is m m. C ("3 .p r»: (eznlmaﬁw a“; ﬁ Part II: 3 points each 11. Which of the following statements is / are true? ,
A. The graph of 'a rational function can cross its vertical asymptote. @Em
B. The graph of a rational function can cross its horizontal asymptote. 7 I
.C. if the function f has an inVerse and f(1) = 7 then f(f_1(7)) = 1. mm   ' . WM) 12“?
_ b. Alonly ' I 
@B only
I d. C only
e. B and C only
12. The inverse function of f is V l" $5 “Eygwjy a X. 14. Which of the following functions is/are one—toone? A.y::c3—a: B.y=lia: (lysi
a. none of' these b. Aonly _ I _ . “M W " c. AandConly I
d. and only only ~ X'HK sawed) _ :15. The vertex of the oarabola I 3562 l 53L" + 9 is. Erma?) ' ' '7 :3: ;mg b..(1,6) _ _ A Ea I 2’3 ' l ‘ . .
(Co (—1,?) t : “MM «a QM) s magmas ' _1,6_)  _ 3mg «5., a} 3,0) ' ' . < 16} What is true about the function f '2 1 .— im—i— a. It has a local minimum eat(2,1). ' I 7 ‘ 1. (i {3&9 '
'  ' i a my ' .
b.. It has a local minimum at'(~—_2,l). ’ _ ' " ' ' . It has a local maximum at (2, 1). It has a local maximum at (—2: 1); . 'None of the above. 17. The demand function for a certain product is given by p(x_) : 200—4m
Where p is theprice in Dollars and a: is thenumber ofproducts sold. What is the maximum revenue? a. $0 assesses». 5%;le 9‘4 Fix) #96 {253539999}
br $25 _ “35” “if£1 win» Elm K
_ $50 ' lam warféﬁiﬁ ; 3.! g: m'_ ﬁmrggggﬁ g $2500 g’é. El}  MW} WE? : r i E? . t I' . = arise ; amt: 18. The following table deﬁnes two functions f andg on the domain
{1, 2, 3,4, 5}: "  
l
1  Evaluate coma—(foam)! = am)  ram) 31—27 . *«QCHfwc‘ff)
—11 a a' «i 3’
c.0, '  _ = ,5 d.1 e. 2 ' _ 19.r__1f f(:r) I 3:2 + 1 and '(f o domain, r 72 Q
a. is 335/2 + 331/2 and has domain [0, 00) kg PM?) '13. is Vang + 1 and'ha's domain (:00, oo) ' =. W 2 +4
(3. is V5132 + 1 and has domain [0, 00) I 7:» ix} + f
d. is m +1 and has domain (—00, oo)_ 7:, x a. g" 7 (a; ' a 3:an _. is 36 + 1 and has domain [0’ I 20. (Banus!) The graph of a function f lies in entirelyin the second
quadrant. If f has an inVerse function then the graph of f ‘1 . . . a. lies entireiy in the ﬁrst quadrant b. lies entirely in the secondiquadrant c.' lies entirely in the third quadrant " lies entirely in the fourth quadrant xsf’fyi . lies partiy in the ﬁrst and partly in the fourth quadrant. MAC 1140, Test 4 B, Part III
Summer 2007 SectiOn number: I 7 Name: '
UF ID: Signaturer _
SHOW ALL WORK TO RECEIVE FULL CREDIT! 1. A farmer has a total of 160 meters of fencing. He I §"'"”“)'g"*”“'
' wants to enclose a rectangular region along a building g X , I wall and also he wantsto subdivide the region into three EWMWWW'
' smaller equal rectangular regions by placing two fences ygnmmﬁmm parallel‘to one of the sides. He does not need any fencing IE" Illllllf along the wall. IIlllIlIIIllllilllil a) Find an equation that eXpresses the totalarea A of the region as a func
tion of the length a: (the side perpendiwlar to the wall) alone. gr ﬁncﬁ. I : +— 9.): we géa :2; a» [£0 ,yx
Volta... : x3, x: is fféQrVx) '
f: —‘f)<'."‘—+ £60K
Am)=.‘.r:.‘fz<.5i.f€=.<?.?i~.p.. b) What value of a: maximizes the total area and what is this maximum
total area? ‘ ' . «if—t) “a
(Rik) _ I .
k 1. Alma arm} :1 estMa + Jaean
at f/SQQ +3.25% we féﬂﬁ
a3: . . . . . . . . . . . ..
Maximum area:....5.;é.€§.Q...fn% . . . . . . .. 7 {mi g. a m» we» 9o Emit} 2. Given the followng graph of the function y = f a) Sketchthe graph of the function y : —_2f + Make sure to
clearly label at least four' points on the graph. ’ «S‘BtlpJi ﬁne. um? I “ SMﬂzﬁn A? 2, vmwhbéé'fg 5 $24}? Qvar xwmé 'xma ﬁﬂm) 2i" «2:.ﬂ1)'«*~ “‘21! $92,.
Kiri6:3 :' vapfaﬂ) =7— ﬁi‘N!) :“"24(°’"} W 2"“ “a. :' w;{f'(‘u.2m+“§) 1?: “amp (.4) 3: Mia» f “'5. “fa.
“‘3‘ “ fzmwsipawawwﬂ M’5 “‘7‘ "2" ‘3. Given the function 2 :1:4 — 4232‘. «1 X$(x%'*?}' 9.; X 2*" {Kai} gigéa) I a) What are the zeros of f? What are their multiplicities? ‘3‘9‘1" i might“ gwwfmm wwwiwimml
mmami? : g ' a 1 b) Evaluate the following two functionvalues: 11—1): [—94 =63  f(1)= r—w = c) On What open intervals is f positive (you may use a table or a sign
 Chart here)? ' _ f is positive onzifTPé‘ﬁ—l (.2. ($3.09}: .
d) Sketch the graph of the function f. Make sure to clearly label all
the points you found in a) and b).  '  ' 4. Given the functiOn 2 . x
‘ 33—2117. ? 2((A'2w) _ 33243: g a) What is the domain of 9‘? Use interval notation! x=t0,x.e%~“f' 3 (eardog‘mégo) wfﬁim} 3' b) Compute the following:%”(—2) '2 ng win 3343) = c) Find the following: Vertical asymptotes: ' x 15:» w; ' .l
. ' . 0% w_ ..
Holes (5*;— and y—coordinate): x r: O y *'—' mg W2;
Zeros (gal—intercepts): g «s: g;
. _ ‘ . l _
Horizontal asymptotes: 7 7“ .7 x i d) Sketch a graph of g. Make sure to show the asyihptotes and to
label the x—intercepts, the holes and the points you found in b).
gi'”?’* g;   ...
View
Full
Document
This note was uploaded on 06/09/2011 for the course MAC 1140 taught by Professor Williamson during the Summer '08 term at University of Florida.
 Summer '08
 WILLIAMSON
 Calculus, Algebra

Click to edit the document details