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Unformatted text preview: Home A {U Tj E VREX‘EJEﬁE;
fiend and follow all instructions. Try to answer every question; remember. a Iteration].r
right answer 15 better than no answer. i. Complete the following deﬁnitions:
1. The domain ofe ﬁmetion is. .. ..
Me; or} 0105, H x  wines. in ﬁlnetionﬂjrjis evenif.... ‘ unit!) 31 3 _
Hr) : lat—x”) or? sweeten gnome
3. The period of a sinusoidal function is l he. Ll —.;§?Jr"i 3. “rut Shredded Junie. Wml 40 Lowlere acted? 4. A function ﬂit) is continuous at a point X. = e if . .. 
{You may use either the epsilon—delta deﬁnition or the limit def": nition.)  VEPGHEMSJE. lei—eh? ‘3? HQ“: ¥Ce)leg at m1 rm ex .54 5., .i _. grim : 4‘ tr“).
ll. Write the heeie formula for eeeh of the following types ol‘ﬁiuetione:
. linear 2. exponential 3. sinusoidal 4. power :5. rational ? E’J‘e
ormwb tJtﬁd“ tJLA9.n(‘de5 Ly)“: $51130 Eyeif Ill. Solve the following equations. Either leave yourenewers exact or round to three
places peel the deeinnel. Simplify as mueh no possible, but note that there may he more .7
than one way to write your mew. Eat: ln{l t2} = Inﬂ) — In{2) = I] : ln{2} = —ln(2] l. lﬂﬂ=25l§ie1 2. my ={4(1§.)a 3. Sﬂ'ﬂ __ 42”: i
' — liw _ Lei EELE '
TZLt’lfg/S‘) K' in {”th “('th )9” '. '
N  9H9 N — 132 7 Ln eowgﬂ'ﬂ
F I H   ##3an
, . .. .'. ' . .‘ . e5 .iLHf
IV. Fmd the followrng lll'l'lltS. If the limit does not most, 'WI'llL DH In.
1 lim ft } 2 11111 ft ) .
. x . x
I—>14+ if; x—}on ____ #0 "In 6x’:r+5
3. —— :—
x—Mo 2—3171 ‘9' V. The intermediate Value 'I heoeem
1. State the Intermediate Value Theorem C1 If] ’fgrpgf fr? IQ] I9 '96:} i5: Cam}.nuuw5 or. a (JOSE
and k i"; 191“; {(3)4VL5) 4hr} JI'LGFE 13 SDW‘iQ‘ Ci” 59.53 533. ffcﬁ‘ak. 2 Use the Intermediate 1It‘aJoe Theorem to show f{.r) = oos(x] "x1 has a zero in [I12].
an {’0' i“; LOP"? Iiiﬂuent”; {Rt—1 (LI. 527 +{L>. ML} _ I )L‘} 'fral): {USESEx?“ ill{0 ___:H_: LIIj”. HIT
JLCID 31'] ﬂ it’d: V1. Use the graph ofﬂx) to sketch a graph of each of“ the following:
1 ni't’x + 3} 3 ftIJ 5 “a
i I sol l. 1iHI. 1Write a possible fimction for each of the following graphs:
I. 2. _ 3. 55“ 1' 9 = JD mitt1 )
VIII. Word thlcms l. A mpﬂﬂy a cost, C is a function of the number of items produced. q, so i. =f{q}. a] Interpret f (5) 23. .
int (o?! in PIOCJHCE {LENS #9 $5366 11'} Interpret f (4E}=lt}. a a; _
Ft: 'i 3 CC] ..»4‘ Uk— {1er I'D. J'é’e’b’tﬁ: riff—£7 FIDO/L. ICE?§;'( c) Use the points from parts a and l: to mite a linear Function tor the total cost as a
ﬁtneetiem of 'lhuB nutulnar “fier1115 produt eral. C q 5
: (I, "I‘ 2. A radioactive isotope decays by 20% in ﬁfteen years. What is its halflife? L} $3.599 {get3V5 V . The LiteIJuedime Value Theorem
1. State the Intermediate Value Theorem. 2 Use the Intermediate 1It'aIuJe Theerern te show that f (1')" e” —1 has a zero in [ﬁne].
£5!) 1‘3 (Eﬂt'l t1HULtS, of? EU“ TI].
mfgf’n“) Ianw ”“1" E—tm m) e' Jz—ILL‘: Statue 3:15]? Luff—.L Se. {.15). 0
VI Us: the graph of x} ton :Letch a graph efeaeh {If the feltuwing. l ft’x 3} P left’vx} : r—— 1'It’II. Write a peeaihle function for each of the following graphs: 4ﬁnn) 7% VIII. Word Problems J
I. The number of bottles of paste eaten by kindergartenete, P, is a ﬁmction of the number
efdaya since school started, LL so P =_f'(ti). a} Imﬂpaeiff?l 1% C‘I {W “ “£111 kttﬁﬂﬁ’ﬂyfqﬂtr liftmfﬁrq 6113“? 6.13%“ l EXH'E h}Interpretf" (1m— 5 __ _
ﬁtting eaten a mar/g: .5;th w m c] Ilse the points from parts a and h to write a linear ﬁmction For the bottles of paste eaten
as a ﬁinction of the number of days since school started. H
t * Ea.  2. A radiomive isotope decays by Eﬂﬂxﬁ in twenty years. What is its halflife? g 5;). I52. é; 1:36am Name Iteacl and follow all instructions. Try to answer every question; remember. a partiallyr
right answer is better than no answer. I. Complete the following deﬁnitions:
1.".[he domain of'o function is 2.1%. functionﬂx) is odd if.... 3. The period of a sinusoidal ftmctlon is 4.31 t'ttnctionfl'lglI is continuous at a point e if .. ..
{You mayr use either the epsilondelta deﬁnition or the limit deﬁnition} II. Write the basic formula for each of the following types of functions;
I. sinusoidal 2. power 3. rational 4. linear 5. exponential III. Solve the following equations. Either leave your answers exact or round to three
places past the decimal. Simplify as much as possible, but note that there may be more
than one waji,r to write your answer. Ex: ln(Ir’2] = Inﬂ} — Int?) = l} — Inﬂ) = 411(2) t. lﬂﬂ=2cm 2. aﬂﬂf =I.4e’ s. lﬂtlrrrc'
x : as so «a 2: in (£7L‘f_)_ a: so We)
":5 i 085; N it’llﬁi'g/lrw‘j 1: ﬁﬁqb
'  . we
IV. Flind the following limits. If this. limit does not exist, write IIHH.
' m1
l'x—lln]4+ﬂx) (l g'x—urﬂxiﬂf Iit‘l‘l x1 l 'x—r—I x+l ._. Q 3 'v“. Th: Intcrmcdtatc Vanna 111mm
1. State the Intelmediate Valua Theorem. 2. Us: the Intermediate Value Theorem to show that fljx) =1 — am" has a Item in [13,11].
fit“; a: Cowlm “at“: m [9.173 m3): tam“. I—e if.) fan) — tram” fat: an at m .3 LE font1) 3i. gotta} = D
VI. Use the graph afﬁx) to sketch a graph nfaaah at“ the ihllawi Lffx + 3; 2.fr~x)  3 VII. Write a passihla ﬁmction for each ofthe fallawing graphs: tJ :: '92th Dig/'4') VIII. Ward Prablama
I. A Netti} hiil, B, is a function of the number of minutes used, I, so It f{t}. R
‘uj — 3:3,: it]; a} Intmpmtftsﬂﬁ) = as _
ﬂu; bi” gar SOD MtﬂLdizg :3. £65 in} Interpret f] (40) = 250. c) Use the points From parts a. and ta ta write a linear function for the bill as a function of the number afminutaa used. . ~t
,5: _1&—t at; 16 2. A radioactive isotope decays by 20% in thirtyr years. What is ila haIiLIIfa‘? 9:, 193‘? agar? Read aﬁfollow all insane—none. Try to answer every question; remember, a partially
right answer is better than no answer. I. Complete the following deﬁnitions:
I. The range of a ﬁinetion is 2. A function ﬁx) is odd it" .
3. The period of a sinusoidal function is 4. A ﬁinelionﬂx) is continuous at a point e if
[You mayr use either the epsilondelta deﬁnition or the limit deﬁnition.) H. Write the basie ﬁormula tor eaeh of the following types ol'funetions:
l. rational 2. power 3. exponential 4. linear 5. sinusoidal III. Solve the folioWhig equations. Either leave your answers exact or round to three
plaees past the decimal. Simplify as much as possible, but note that there may he more
than one way to write your answer. Ex: int] f2) = lnﬂ} — 1n(2)=i}—}n{2}: ln{2} I. 2 = 23‘ 2. 1eH = 4 s. 10(5): : 3(4)‘
Xl‘tti :——h—'_‘i‘i ‘ f fiffe’)
' i it"! KL." "H ' '1 e was 2:: =:::m W. Find the following limits. Ifthe limit does not exist. write DNE. ' Jim
1 hm .ftx} 2. fix]
x—H 'v'. ‘i'la: Intermediate Value theorem
1. State the Intermediate Value 'I‘heorem. 2 Use the Intermediate Value Theorem to Show fix): oosx— —2x haeazero 111 [ll 1].
Qty1} 15, com I. r'f’ILAoLae can I}; II tap) teemLjIe—e C(ltcsIQrb 5;; I333 Ir'l 3 e 11' Icin— It: 3 U
VI. Use the graph of ﬁx) to sketch a graph of each of the following: Ifrxl+l new; VII. 1I’v’rito a possible ﬁsnction for each of“ the following graphs:
1. 2. we. Word Prohlenis LI I. KJEJ‘KI‘F"$YK_ ”11) I. The total profit, P, of a garage eale is a function of the number of items sold, t1, so
P 21“} a} Interpretffeﬂ} = m L? LID Hams ere sold, hmerégl }e Filo.
1:} Interpret r 3o1=12a 1' W ptoyll 3g $30,, I510;'fohsuor€ Solcl. e] Use the points from parts a and h to “Tito a linear ﬁmotinn for the proﬁt as a function of the number of items sold. 1:) I
3." If]; 2. A radioactive Isotope decays by 23% In thirtyﬁve years. What is its halflife? [0% at} 62(23th Home Read and fhllow all Emotions. Try to answer every question; remember. a partially
right answer is better than no answer. 1. Complete the following deﬁnitions:
l. The range ofa function is 1A funetionﬁ’x) is even if....
3. The amplitude of a sinusoidal Function is 4. A ﬁmetionﬁ’x) is eontinuous at a point e if .. ..
{You may use either the epsilondelta deﬁnition or the limit deﬁnition.) ll. Write the hasie fonnuia for each of the following types of functions:
1. power 2. rational 3. linear 4. exponential 5. sinusoidal III. Solve the following equations. Either leave your answers exaet or round to three
places past the decimal. Simplify as much as possible, but note that there may be more
than one way to write your answer. Ex: lrufl f2} : In{i} — mm) = t} — ln{2) = — lnfﬂ} t. s=sser 2. ltli3)‘ =2.5[s}* s. 5‘” =34 ELF
X f [In 5:3 «f e .3ng? "it, : § 1:: SJ.
:5 *33’31 a ram s: tip€333 W. Find the following limits. lfthe limit does not exist, write DNE. 1‘ x 1—1;“qu [Ii 2' rim—sfix) W E r  l x w} t} sin(2x) J.. :1 lim .1: ll. Name AN iv” E Uﬁ “331:3: 115?. T7 (“is Read and follow all instructions. Tr};r to answer ever}.r question; rcmornher, a partiallyr
right answer is hetter than no answer. 1. Complete the following deﬁnitions: I.Tlterangeofaﬁmtrtionis.... slit; {£4 Dru?” PC'FESr—iﬂiﬂ VclIrLléf’ﬁ c. {S MAS. deewndo H 'l' U Ett‘ t e? is; i at
2. A thnetionﬂx) is odd if" . . . I .
10ml . _ it.) a» sinMm— stxul a. s 3. The amplitude of a sinusoidal function is .. .. . z) . . I
lift it? Jl‘LQ‘ Ci ifiv'ic‘itsfff tanI J lit»; W} r rs .m u. 1W1 +4: “(,3 ﬂqﬁy, Jr'smm I
4. A ﬁusctienffoI is continuous at a point e if
{You magir use either the epsilondelta deﬁnition or the limit deﬁnition} II. ertﬁ the basic formula for each of the Following types of functions:
1. rational 2. linear ."l. exponential 4. sinusoidal 5. power ill. Solve the following equations. Either leave your answers exact or round to three
places past the decimal. Simplifyr as much as possible, but note that there may he more
than one waft.r to write your answer. Ex: In{l i 2} = ln(l) — 111(2) = 0 lot?) L —ln[2) 1. 5n = as“ 2. 20m‘ =L4t5r 3' 53"“ = 4f r
‘ ‘2' _ L'ﬂ la. 23'
K: brig/5) F1: Eli All) 7‘5” (1:75— +Ll _§
w . LH 52'le _ _ c'
£59}.le e; Eric} :3; 02.6;
W. Find the following limits. if the limit does not exist, write DNE.
lint lim
1. 2. x
scold—fix} 1 x—r—oeﬂ: 3" ll
— I
3 lim x—l H \
xmacoz x ...
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 Summer '08
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