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Exam2_Solutions

# Exam2_Solutions - M 305G Exam 2 March 5 2008 Name 1 The...

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Unformatted text preview: M 305G Exam 2 March 5, 2008 Name: 1. The function F (x) = 3% has an oblique asymptote. (a) (6 points) Use long division to ﬁnd the equation for the oblique asymptote. 2x_2_ #‘ﬂh—W X2+\ libs" ~1x1+qbf “'3 «L1x\$*1x) "sz t-X ’3 “(‘1x2—23 X ——l (3.15:; x3: 1x~L // x—I 7% H20 _ 2"“7-+ x144 (b) (4 points) F crosses its oblique asymptote: find the point Where this happens. Mews 1-. Makes 1.. 333:. ALL MMFAQF‘ as an; M Shh-Q Star x: X’s a 1: 2X”Zi—X*L,‘_ =Qx~L X ‘ O \ §°lv¢ gar x: Fc:«>—.—.2x——2. :2) K I a» X ‘“ X2“: 3- :23 x-\ ‘2— o “’- l (c) (3 points) F is in lowest terms. Does F have any vertical asymptotes? Why or Why not? No. \le/rln—UAL ()‘gWX—cks Cod/x mixﬁ OCCAM" WW k WWW \s 37:015- M 2- _. X 4—\ "O m N6 REAL \$6L~UT1LTNS PagelofS M 305G Exam 2 March 5, 2008 2. Let g(:r) = m2 + 2:1: + 3. (a) (14 points) Find the vertex, axis of symmetry, :5 and y-intercepts of g. Oxt“ \ \e =- 1 C: “em“: 9%) %(—§'O\\\ 3 j 3 ll ”””””” —.b Xe” aw“ i ”\ x “grbqvthzc-«ﬁzemz - \-l+3:’2_ w KM X W: X=~'X .Hﬂx— f—f—g (05% (o\\ 2 305) = 3 M\ X‘;A‘\'5Mm,e Wis \s ham 38% W9“ \éf’iazkh is CK ?0Lm\96lo\ +549“ Ms lag m3 \mo-b “‘91ka w. 1A<\So'. \Q )(Z—erArZ’szo “Ram X: “Bit—hm —Zi\l"g (b) (10 points) Draw the graph y = g(x). Label ﬁve points ofthe graph. Na £05. Sgkm W «€ka (4,2) M k ‘g—mk— L039 Mara SSW“) ‘wx ”9““)? (05. 31%; Hi God: (3, 984M- \5 x=—\) \5; (5,3) is “:5 (._ 3) Q m W€\n) JAM—m 5a 13 0.2) 3) We. CM C‘AWQ‘XR (303 5m SEQ Page 2 of 5 M 305G ‘ Exam 2 March 5, 2008 (c) (8 points) Find the points where the graph of y 2 ~33: — 1 intersects the graph of y=9(\$)=m2+2m+3’ Tex; we“ ‘\V\MQ§\~ lel‘c A‘k Q‘WQM \$b\\rC—Qsc x1 owe. QM' XZ+1X+3 :2. sax—4 m 75ka 5g. ! :9 X +Sx +L—\ :20 W Okay—ﬂ» @Q‘Wchﬂ‘b (~\ =3 (X+H\(X+D= g B 0x 3%C‘H32“ ":5 X: “L1 or x=~\ XPA\$51 “3 (“\3’\ 3‘3”&\:2‘ m Enema—C Same“ WK\$ be -—3 W34: \1”\¢-\\ l 2. ‘ xg—Er15\—-H-‘1-\ = —5—_\;ﬁ So (,\)2‘\ QM; C—AJ\\\\ ' 9. : —5*-3> -—8 4. ‘_ CL ”“ ’27“ ’7: ” “Liar" 3. (7 points) Let f(:1:) = «42:5 + 2x2 + .2: — 3. Find the degree, end behavior, and maximum number of turning points for f. Page 3 of 5 M 305G Exam 2 March 5, 2008 4. Let g(:c)= x2(m — —)3 (:r + 40“. (a) (9 points) List the zeros, and their multiplicities, and whether the graph of y : g(x) crosses or touches the m—axis at each zero. Zeros mw\¥re\1c\\'\e; Jaws [m3 ' 1 Walk 3 O ,L 2‘ Crass “'1 Li 1m» (6 points) )Find the end behavior and degree of g. Aegﬁzpc 21-31% 2 Ci (c) (6 points) 6 Sketch the graph of y = 9(17). Page 4 of 5 M 305G Exam 2 March 5, 2008 5. Let 2x2+4x~6 _ 2(m+3)(x—1) 9102—36—6 _ (x+2)(x—3)' (a) (2 points) Is R in lowest terms? Why or Why not? H231“ puma-Aer aw) W1M§u~r how: was Casvvxwm mks/RR b)(2 points) )What 1s the domain of R? ES §XeR\7s +4J><¢33 (C) (4 points) Find the x and y intercepts of R. \ _ .3 7- *— m"(°1kib\3 a: Rik) == 2%,,\ \w ROG-O > 27g Arm 5:0 L \ =17 thabumzo a.» “kg th=\ 1,; PM w» (d) (9 points) Find all the asymptotes of R, and any points Where R crosses or touches an asymptote. R(3:) : ﬁle’Z‘A—qx’ﬂy =— AL6LXZ~x—Q\ 8° RA (5112? 7‘9— Wk: 2; L3 1 To 11 R “was an, save Rho-11 =9 X 7, 1X *HX—621 :2) 1X +L\7( “Q 7: 2‘}?! ’12} ’g‘ 7:? H%”L) 7: ’ZX‘Q x1~><~e (e) (10 points) On the back of this page, draw the graph of y = Rm). Page 5 0f 5 ...
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