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Unformatted text preview: Be sureto bubble the answers to questions 1 through 20 on I ur scantron.
@ _ . Part I: 2 points each ' In problems 1 through 5 indicate Whether each of the folloirving statements
is true or false.  ' 3—1 1. The'two funetions f : $—_1' and = 1 have the same graph. g Riki; £334... :3: f aér _ ! 2. The polynomial function : 3(m — 302(1): +3)? has a zero of mul—
tiplicity 3. . ‘ ' r True
 ' alse \  The polynomial function f z 3323 — 3:21 + 133:2 — 1 has at'most 22
turning points. ' (a) rue
(b) False 4. If f and g are any two functionsthen f o g = g of. (a) True 3‘2?“ I 18 "5th ﬂexirl : . A ' I  . g' I “2.”
"(b False '_ 7 (pal) (x) == 5053+!) ﬁ {34”} 3’“ grim;
 .  f.  {amQM = Wis 2'» Mt +6 5. The parabola with the equation —5(3: 5— 5— 3 has vertex (—2,3). ' . 
True '1). False 6. ‘On _Wh1€l1 open interval is the function 2 ~—5(ac + 2)2 + 3'increas— ing? 1 5 ' 1
@ (Moo, —2) ' b (a2) ~ ‘ c. (—200) . __ ' it...”g '
d. (23 00).  7. The average rate of change of f z 2 — m2 on the interval [1, 3] is 8144 » Mai“43(1) g as} "tilt“i3 C9 4%
'—4 __ s a} .“ 2rwa ” 2;,
C. 1 V m «5? s I
. a. W. x “if; d.—1 ' ' '2“ '8. _Whieh of the following functions has the same end behavior as = 1:3 p
and crosses the :c—aXis at the origin? . a. If(3:)7: 23(3 +123)(3 — 13.: 132(3): + 3) I
©ftv) : 2303+ 3X2: ~43)
I 61.1133): $28 '— 93) 9. The function f = £9233) has .a’ i «E
Blame, *5 hammers?» a. horizontal asymptote y: 0 _ 3 5 " horizontal asymptote y f—" 1 (3. horizontal asymptote y': — [0120' (1. no horiZontal asymptote 10. 11. 12. '13. '  a} (—2, 1) If ﬁx) :I x/7 x — 1 then What is the domain 'of f’A?
[0, iaméL‘ﬁ a? .p‘.’
b. (—oo,0]  _
=3— rwyﬂek mi”. ,5? e. [1,00)
' d; (“400, 00)
Part II: 3 points each Which of the following statements is / are true? _ A. The graph of a rational function can cross its vertical asymptote. ﬁllsa
B. The graph of a rational fanetion can cross its horizontal asymptote. .Me.
C; Ifthe function'f has an inverse and f(1) = 7' then f(fﬁ1(7))' = 1. ' F . [5‘ ‘_ "if I . «Psi? W2; =«v "F a. ' none e. B and C only ' _
The domain ofﬂw)‘: V'asg—LE—2is' X‘fo "‘39 b. [—2, 1] T he inverSe inﬂation off 2 is
y Mfg,“ 14. Which of the following functions is / are one—to—one? A.y:a:3—;r Byzlxl C.y=li a. noneof these A:
b. A only I 34¢ c. A and C only 3“
d_ B and C only f; c only x3 x :WW b‘ (176) glﬂy . (“"112) ~' I it :2" “gig”? $3 Eléweéétré‘le“?
e.' (3,0)  ‘  I a '16. What istrue about'the function 2 1 — + 2? a. It has a local minimum at (2, 1). I b." It has alocal minimum at (~2, 1). r I ;' c. It has a local maximum at (2, It has a local maximum at (—2, 1). e. None of the abOve." _ _ 17. The demand functiOn for a certain product is giVenby p(3:) 2 2007—43:
Where p is the price in Dollars and a: is the number of products sold.
What is the maximum revenue? ' ' Erik) .‘’~— X Hm)  =5 x {1cm mtgﬂi} a,_ $0 ' caveman: :
b. $25 '3 « S4 x1 r Emma
c $50 gum Wink}: 5'? h “2.06:: W «£5338 I {a Ens} its?) '7“ 7
(:1 $2500 i ,1: I I
(3. $5000 Rag") “3.: ZS" “3.25) if
p.)
i";
.5
e
W
'5"
5”;
_@
9 :6. 18. If ﬁx) 2 562+ 1 and g(:c) I {S/ﬁjthen (f og) gamma. ; as “3.53 a. is m and has domain (—00: _ Q3": dwarf?) b. is W and has domain [0, . _ ‘3 VT 2‘” a» f c. is :13 +1 and has domain (—00, o0) ‘ “$7 has? f p
is 3: —§— 1 and has domain [0, 00) g' a: «2'5 5 (/63; 9‘3 3:3) I e. is m5/2 + 561/2 and has dOmain [0, 00) 19. .The followingtable deﬁnes two functions f. and g on the domain
{1, 2, 3; 4, 5}: ' Evaluate (fof)(3)—(fog)(5). ia w a.—.2 I I _:“.,i?(:} ''r§~f§”?
®_1 Him; W c.0 . 3mg ' d.1 8.2 20. (Bonus!) The graph of a function f lies in entirelyin the second .
quadrant ._ If f has an inverse function then the graph of f f1 . . . a? Ia. lies entirely in the first quadrant
b. lies entirely in the second quadrant
0. lies entirely in the third quadrant @lies entirely in the fourth quadrant
e. lies partly in'the ﬁrst and partly in the fourth quadrant. MAC .1140, Test 4 A, Part In
summer 2007 ' Section: number: . ' Name: _
. UF'ID: I '  Signature: .  SHOW ALL WORK TO RECEIVE FULL CREDIT!
1. A. farmer has a total of 160 meters of fencing. He _ §"'"""lﬁ""""
wants to enclose a rectangular region along a building g X
wall and also he wants to subdivide the region into three Emwmmm"
smaller equal rectangular regions by'placing two fences ' ygmmugﬁmm". .
parallel to one of the. sides. He does not need any fencing g '
g x along the wall. illllllllltlllllllil a) Find‘an equation that expresses the total areaA of the regiOn as a func—
tion of the length :1: (the side perpendiéular to the wall) alone. ' ‘ lanai” {3’5 ﬁrm» I r r raw: {as ==> yeaawrx
obese... : Ky. I .2; 'g'fggg '5 “ifth “r {QC} K . A(¢):..:i‘>€f..t..ié®.
r b) What value of r maximizes the total area and What is this maximum
total area? ' WWW W. verse}: 6
avg) 24"?) k = as) w arm} a “exam was as: “lease Sane lama. . . . . . . .33;
Max1murn area: ENE; . . . . . . . . . . . .. 7 (are ye {sawem s EC? 5's“: 2. Given the following graph of the function y = f a) Sketch the graph of the function y :_—2f($ _+ I). Makeeure'to
 clearly label at least four points on the graph. ' ° eke‘fé' ane. Lewis? @1635” Q 3?; i 9— .
3;"
3‘9“? «a! = Flame) "=5 we} gamer. mg ; Maw; wékﬁe‘; wife) E & ﬂew1 9. wznm 959g} ﬁ‘ﬁgifﬂ) e. a»; q x: wag”
We ~‘ = ewe); if “we “g e mi, 3. Given the function = 274 «_— 4382. 3 x2“ Wave”) “4": xii? ‘3}(Xt3vgl a) What are the zerOs of f ? What are their multiplicities? a‘ Wig? , Gm mui‘ﬁpﬂ‘ﬁg‘ﬁy _ W7 I
b) Evaluate the following two function Values: ' I
f(—1): new :2 W3 f(1)=_f"f'1 we 0) On What open. intervals is positive (you may use 'atable or a sign
chart here)?‘ ‘ ' 3 $2 a {mmXi?» «: 7 f is positive. on: (TQ’i;.T°ﬁ2).i#.{3inz . .
d) Sketch the graph of the function f. Make sure to clearly label all
the points yOu found in a) audio). _‘ 4. Given the function . _ ' 332«—I2$ a
go) a 2 . a ‘ a) 'What is the domain of 9? Use interval notation! .'
Ma Hz; #2in : (“mapf) 3.: (4m) o (aim)
bJCom ‘3 —I 3' '__ f 3' "nl'
pute the follow1ng.,f’(—2) — é!» 4’11) _ ——a: 49(3) _ 7;
(3) Find the following; I ‘
Vertical asy‘mptotesﬁ X  .. g
Hl' 'd (Igl'ti  .w"9m:.€rw.._gn
0 es (:13— an y—coorina e)_. I x : j 7 {LEM w
VZGI‘OS (ii—intercepts): X 727 _ I Horizontal asymptotesz y a .  d) Sketch a graph of g._ Make sureto Showthe asymptotes and to
label the w—interoepts, the holes and the points you found in b). .Xéf‘l
2“ "I ...
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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

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