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Test3Solutions

# Test3Solutions - Math 108 Exam 3 Name,ailws wags Fall 2011...

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Unformatted text preview: Math 108: Exam 3 Name ,ailws wags Fall 2011 Instructor - Calculators are not permitted for this test. Ina-IMMEWMI — Show all work unless the problem requires only a short answer. - There are problems on both front and back of the pages. - If you need scrap paper, ask your instructor. You may not use your own. If you do use scrap paper, make sure to hand it in at the end of the exam. 1. (7 pts.) Find the solution to the following system of equations (use any legitimate algebraic method): . €5le 1375+g~12 2’26“ng {g_;=8 t;f¥::ji:;g~ ZQ)’@‘;§ C3,’L) E ‘% tw * 4:2;2 %;ftc 102:2; r3 2 ’ possﬂota. 2. (13 pts.) Find the solution to the following system of inequalities. Show your solution using a 2 graph. Algebraically find the coordinates of all vertices of the system on your graph. Mark these E points on your graph- {33;ix22x:31 Verb cm 1 ZhﬁwVZX’i W313“? met/922754 gXZ—ZK”830 (27d LOOK ~13 :0 7L: it; x: L 3. (6 pts.) Solve for x: I5x—7l—x=3 ll €X¢710 LC 970-740 @L'buﬁ Aom l5 S'K’7"7C;3 (3%th H ”(51‘7)“Xt§ 47(le ”§X+7~7C:3 .. lu Xv q 'él’t’cf ~ a Z ._ 5,7: / X“ “:2 / 4. (6 pts.) Use absolute value notation to express the following: (a) The distance between x and 2 on a number line is at least 5. blgmcg betwuﬂ a a») \3 is 8“,“ \aa \&”\0\. S17: K~2l E 5‘ (b) The set ofxin the real numbers indicated on the number line below. «if < K < Z + l +i +| H—«t—H—A—ﬁ—l-ﬁF-t—W w3<x+l<g —5 -4 -3 —2 -1 U 1 2 3 4 5 lx+il43 5. (6 pts.) Graph f (x) = 2” —— 5 on the axes below. Label all intercegts and give eguations of any asymptotes. We» 6. (20 pts.) Solve each inequality for x. Express your answers using interval notation. (a) I4 —- 3x] < 11 1? wH< 4'27C<t( (.33 g) g" > 7C > 4i} (bug) 61+? >»§2c aszt __ IS <)C (/7C>_§ («5—1 00) 3L2X+l§>~§7t 76> TE” (0) x3—5x2—6xSO M13351 ~63) £20 M tho/QM“) :0 -—( o é Qxeﬂeéﬁim QM UAR“? 9:3“ (Pm/“’1 UE-O/ 6] mm x:o/ tté/ Kc ’1 (d) x3—5x2_0 \$2.23 > o ’i’ - ‘ “'" a + X (X’ (A i “Z 0“ ft QR N949“ WQW 9 [A ‘/ :W 1251/ ”KEG, 1‘5 (”mIAZ‘] U (LS/100) 7. (20 pts. — 2 pts. each) Evaluate each of the following expressions involving logarithms. Simplify answers as much as possible. (3)10gaa2=_ .VQ. <b>logb§= fl- (c>log71= O (d) 310%6 = __é_ (e) log3 72 — log3 8 = i (f)10g4 642 = A (9)10g5(—25) = Md} (ogrhr‘sl'lxnl‘x‘? erwigke iglbg‘f 6L] 7; 2C3“) '3 A ALS'L a] 9 Q ‘ 3 n (h)1084 8 = “’7: (i) logs 81 = i (1)851“2 = it logs 3 , _ a , 5. eff; 21:3 0M2 0.; Led/6 e51A2~ AZ 226 2 ~ 3 lo .is‘l 1M1G69’8& A 6 Z : X”; 6&3 {035’} £614 3?. .. 8i 1 7, 8. (10 pts.) 1°?» L{ 32 (a) A parabola with vertical axis of symmetry has vertex (2, 3) and goes through (0, —5). Find the equation of the parabola. J. (2"- [4) 2+ k SW”! 49““ 3‘” e-tlwl‘b'r" 9“ in” . . z Ve/HX (2.13) (=9 Luli kzg‘. (a: \$LK’Z)+3 New 7“!) 14m) P [Cl/‘01.» W4 [0/ ’5‘} 12 CL (of/ML \$91] ’5’: gleam; gm 42 M {>\$"§/ é? (13;;‘2' 2.. Amswr “ ‘6 : ’ZUC”2-> + 3 (b) A parabola has vertex (4, 2) and directrix x = 5. Find the ordered pair representing the parabola’s focus. . A NWLRK VQI¥€¥ {4 W M1} QM Ji‘mlw‘x (1:) mg; 55 pm? umi’ 45M ng [A Mu Ohoosfl—e thw 7’11! A, We [3,13 is “W ‘Qwué. 9. (20 pts.) Solve each of the following equations for x. (a) 25" = 5496—5 523: ; g 1/ 76"296; 3'7! - ”gt/39 ~é (0)10g5 x + 10g5(x _ 2) =10g5(20 _ x) [OQYOCQC’LW Z-[DéﬁsCZD’YO 1?” 296 = 20 ’76 11-» 7C ’20 :2 0 C7: xg>c2c+q3 :49 {m 7C : “(ﬁe—“0+ REV/mu “1535K, £0 raga/5c (d)5‘:5=6x+1 om; M ma «» mw W W» 1 ghmixhcﬂt”) ggté Ma 5 ’J2«w{ :LutM/«é €524 47m UN»? 'ﬁAL( ' XﬂxlaJrﬂ/xlg S4: 4/ é 6x ’Kln5’~7fjné :Aéhé4 SK / _,. 3 2% xéﬂns/ﬂﬂéwmww N , LQJWZAL! [EK229/ ...
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