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 = 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) *qu t-X ’3 “(‘1x2—23 X ——l (3.15:; x3: ZX_L // x—I 95 H20 _ 2"“7-+ K2+l (b) (4 points) F crosses its oblique asymptote: find the point Where this happens. Mews 1-. Makes 1.. 333:. ALL Mmfikr‘ as an; M Shh-Q Star x: X’s a 1: 2X”Zi—X*L,‘_ =Qx~L X ‘ O \ §°lv¢ frat x: Fc:«>—.—.2x——2. :2) K I a» x ‘“ Kit: 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. Osawh—cks Cod/x OCCAM" WW k \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”: (—‘zb'an %(—§'O\\\ 3 j 3 ll M “ fl ’ —-—- —.b 2k” aw“ i ”\ x “grbqvthzc-«fizemz - \-l+3:’2_ KM 63 “are .Hxx— f—f—g (05% (o\\ 2 305) = 3 X‘;A_\__:Mm’e Wis \5 ham 38% %=8Q<3 is CK ?0Lm\96lo\ +549“ ms we m3 \mo-b WFRX w. 1A<\So'. \Q )(Z—erArZ’szo “Ram X: “Bit—hm —Zi\l"g (b) (10 points) Draw the graph y = Label five points ofthe graph. Na Sakm W weka (4,2) M k ‘3"“-\—- L039 Mara 1A 1"”)? (05. 31%; Hi God: (3, 984M- \5 x=—\) \5; (5,3) is “:5 (a 3) Q m JAM—m 5a 13 0.2) a) we CM C“\°"”Q‘*R (gm 5:1: 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; \vwair lel‘c A‘k $b\\rC—Qsc x1 (mo. aw. XZ+1X+3 :2. sax—4 m Tbmk 5 :9 X +Sx +L—\ :20 W Okay—fl» WK‘W33W9 (~\ =3 (X+Hx(x+nz g B 0x 3%C‘H32“ ":5 X: “H or x=~i XPA$51 “3 (“\3’\ =‘3"&\:2‘ m Enema—C Same“ WK$ ice -—3 W34: \1”\¢-\\ l 2. ‘ xg—Er15\—-H-‘1-\ = —5—_\;fi So (,\)2‘\ GM; 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. m \maimt— Wm Ag >4 as 53 a. \A48_(Sr\:5‘ gnaw; QM ) a; EAWW \s me m (w “WEB Wx‘wwx “my J8, *UPAW‘%?OMX$ i“ S”\ Page 3 of 5 M 305G Exam 2 March 5, 2008 4. Let g(x) = x2(m — + 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\‘xc\\'\e§ Jaws [m3 ' 1 Mat 3 O ,L 2‘ 0x555 “'1 Li W (b) (6 points Find the end behavior and degree of g. ) A¢3j3\ :2 1+3+U\ : C1 (c) (6 points) 6 Sketch the graph of y = Page 4 of 5 M 305G Exam 2 March 5, 2008 5. Let _ 2332+4x~6 _ 2(m+3)(x—1) 9102—30—6 (x+2)(x—3)' (a) (2 points) Is R in lowest terms? Why or Why not? k19€$.—TL'~ hawk“ aw) Amwth how: was easwxwm (‘ofik/Qéfi. ROB) (b) (2 points) What is the domain of R? (c) (4 points) Find the x and y intercepts of R. \ _ .3 7- m— m " (DJRLUXB a: == 2%,,\ \w > 27g Arm 5:0 L \ =17 ZCMsSum—ao 1.; “kg flxfl PM M) (d) (9 points) Find all the asymptotes of R, and any points Where R crosses or touches an asymptote. 2. fi<1x1+qx#c) 1'— ALa‘LXZZ-X -Q>\ gt’ (g: T 29‘ Wk‘ 3 L3 1 Ti) See \S— R mwdfi (8:1 x %\‘K‘ ROG) :7“ {GM X 7, 1)“ “ix—6:1 => 1x +14% ~(o = 273‘ ~2x $1 7? Hump = flora x1~><~e (e) (10 points) On the back of this page, draw the graph of y = Rm). Page 5 of 5 ...
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This note was uploaded on 05/01/2008 for the course M 304g taught by Professor Blass during the Spring '08 term at University of Texas.

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

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