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**Unformatted text preview: **[Cg/ll (QOOG ‘ Examj So/u’f'forzs 1. (6 points) Mark each statement below as true or false by circling T or F. No justiﬁcation is
necessary. If f is an even function that has all real numbers in its domain, then f is not
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y = f (23: + 1) must have a vertical asymptote at :r = 2. (’th‘AL «goal Low Staph +mms€rM$-) If the graph of y = f has a horizontal asymptote at y = —3, then the graph
of y = f (—13) — 1 must have a horizontal asymptote at y = 2. W CONECT aSympf’o‘fg in p/acg a“ uyca‘z" SAW“ 61 “/y:—-§¢f/‘. age/h +£8.24
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35 ——4~ when r = 3, the Intermediate Value Theorem can be used to conclude
that f (c) = 0 for some 0 between 0 and 3. ’P lies a ae‘SNM’ylinUr'ﬁly off X5!) 50 ﬂiﬁj‘V/‘Q‘Md 56 “lop/160?. The graph of y = $2006 has an inﬂection point at m = 0. 2) y’aQOngwos. mag y’/:;?ooe~;zoo5x”0" >0 4;, 41/ #0
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then explain Whether it is 00 or —00. (a) hm 3:07 — 5m + 1
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expressions as slopes of secant and tangent lines, list these quantities in increasing order (from
smallest number to largest). No explanation is necessary. f(0-5) - MD M) — W) o 0.5 f”(0-5) ﬂamed "ﬁler 55‘ “W < 1°70 “Ftp—Ff!) < N’IQF O < €705).
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(a) f(a:) = 4232f -— 893 + \3/5
= foa'; " 8K 'f‘ ’sfg‘l J, so) «NW +695)th - 2’ + o = WK 8 = 10. (5 points) Let 9(1)) be the fuel efﬁciency, in miles per gallon, of a car going 21 miles per hour. (a) What are the units of g’(90)? Miles V) milesperﬂwr’ (b) What is the practical meaning of the statement 9' (55) = —0.54? Give a brief one— or two—sentence explanation that is understandable to someone Who is not familiar With
calculus. Matty answers are acceptnéla. t‘ére is (134E, PCS-535% Pl‘MSIL’S 5 When ﬁle Cari: 509601 ‘5 55 miles per hour; ﬁg rm? éfcmﬁge Q70 £6]
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Q‘Fﬁcieyzcy (anal vice llama/3) a‘f an appmﬁma‘fe m'l'g OTC 0.5771 mp3 Per MFA. any small immense m (Coulal say “513860” or “Klocl’fy 11. (8 points) A function f has all of the following characteristics simultaneously. o The domain is all real numbers except at = 2, and the range is (—2, +00)
0 lint; f = +00 0 lim f(:c) 2—2 and lim f(m) =~2 x—>+oo :I:—>——oo
o f is continuous on (—002) and (2, +00) 0 f is increasing on (—00, 2) and decreasing on (2, +00) (a) Sketch a possible graph of f below. Be sure to label the scales on your axes. One possible answer: (b) Give a possible formula for f. (Hint: think about transforming the graph of a familiar
shape.)
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