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Test1Solutions

Test1Solutions - Math 108 Exam 1 Name ANSWERS Fall 2011...

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Unformatted text preview: Math 108: Exam 1 Name ANSWERS Fall 2011 Instructor Total Course Points - Calculators are not permitted for this test. - Show your 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. (18 points -— 3 points each) For the following six questions, choose the ONE BEST answer: a ‘ﬁ _ 5% = 27 E E E E E E a E E E , When written in its equivalent fractional form, .ﬁ 2 (can 1* 24\$? 4 z :77 3 273 E 27 1 26 F (a) E (b) E; (C E (d); (6) none of these (3x — 5y)2 (a) 9x2 — 25y? (276 373/)CZZ “313) E (b) 9x +25y2 ,W E 35/ (c 3x2+25y2 71C M:l§79 d ‘6 (Mac —30xy+25y2 : 9x Z’ZQ’ZB tlYiai (e) none of these Which is true about the following set of ordered pairs? E {(1,2) (~3,_4_),(7,0). (2,3).(5.—1)} , (a) The set represents a function having an inverse function. E @The set represents a function having no inverse function. E (c) The set does not represent a function. (d) It cannot be determined from only five points whether the set represents a function. (e) none of these 3 is an example of a function that is: f(X)=W C )3 .. Z; 18 } dd 4C) 7* ”/1 1 '1 ’ (K ﬁven 7CC W W (0) defined for all reals (d) symmetric with respect to the y-axis (e) none of these E? @:;W After rationalizing its denominator ”I" r err (a) 3% (b) 2\/—2- @3§/Z (d); (e) none of these Suppose g(x) = “:2. This function has y—intercept of: (am-2) 0 140* I'“ 00M“- (b) (-2, 0) ’ (c) (O, 12) (' (0,18) (e) none of these 2. (10 points) Simplify the following as much as possible. Express your answers using no negative exponents. a) (—Zab'2)(——3a4b5)3 w- is" - i3 ’3’ E Z~Zalo 7-”Z7ﬁllé Z SILIlﬂ b I . ,9 4: . t’l- 1° : b)(2a4b-3C2)3 : w 2 C (2a3b2c -1)4 [175/2 bgcrq 2 Q :7 3. (14 points) Combine and/or simplify each of the following expressions as much as possible. Specify any necessary domain restrictions 80W : Jgtzgz-lg : 223JZ~3 H N %l \$3 l “v n p bH/E—i/ﬁ E g f l E i i 3 § E ; i : ~ 3 z i i (IMXm—Q “#00650 x2+x—6 x2+3x—4 ,. C) * (mwtxwvcwﬁéz A2,) l . t; E: Z #1 ”((1 _2/ a E {#2, / i 2(t+z> d) 4. (24 points) Solve each of the following equations for x. a) x(2x+5)=12 sz+§x~1130 szw33Lx+€l) :— Zzwgco m2, 75+‘(3’0 z»; m rw b) x3+3x2-—4x——12=0 kKuz) “((20—3) = are; XXI» C!) T; CX'FB 7~)C?C+—23C?C"L)O' X=~3 X ; *9» {:2- c)\/2x——§+W=3 275’s? ; go—W 21—:97véW—FI HM Z’xw-g’ : x +Lo ~6J—i—{Tl x 45’ = ~edﬁ7 7C"——3’07C 4475’ \$340090 3x+7 x+2 gm}? ‘9 x0923 : (75—9217 2m? #78944 i 3?” ‘3 755L132: +7 = 39(“ é Il—PL’K‘PL 1‘9 (“13(sz C 0 1/:- “I, +x=3 zlrééxﬂg? ’v 0 (ram ~33 3 0 Joe; 1.9+ aha/’5 5. (8 points) Use long division to divide (3x4 + 7x3 + 11x2 + 35x —~ 20) by (x2 + 5) z z+7z ~ Lt ’K +s’lgzqr7z +th 2+a§76~ 2&0 ,3; Hit) 6. (8 points) Write —4x2 + 24x — 31 as the sum of a perfect square and a constant (i.e. change the ax2 + bx + c form of the expression into the a(x —— h)2 + k form). ”ﬂint/2642 = ~4<xl»é2c) «gt : -L{(x‘«é?é+9 ”9) ~§l =2 'V(1»3)&+?é “‘3‘ :: ~9/L‘7/w3Y‘ +8" 7. (10 points) Given f(x) = 3\/2x — 1 (a) (5 points) Show f is a one-to—one function, using the definition of one-to-one. 45mm +763 = {C6 ') 3/2217 :— 325:7 Za- { a 2 b ‘” / 24 :2 2;. a = E / (b) (5 points) Find f‘1(x),? the inverse function of f. 2’16 * 1 ‘fr 7C: i/Z‘g—T \-—(C> _. [)fg-i"(~ "’15: ;Z%’/ ‘9 X a 2/ K K...”— 3 +(:Z‘3 2+ i _ Z“‘2S 8. (21 points) The following questions refer to functions f, g, and h below. 3x+1 ifoO f(x)={: ifx>1 __ 1 i 9(x)—x_3 i E h(x)=\/x+3 g (a) (2 points each) Find the domain of each function. Write your answers using interval notation. Domainoff: 956303 U“! 00) Domain of g: M) v? 5%) Domain of h: l l l _ (b) (2 points) Find (g + h)(x) = (5C!) 4' 'AC’K) C X ,. 3 + T {’3 . i (c) (2 points) Find (goh)(x) = comm) 3 3 U 3“” ) f" x/XV’Z ~3 (d) (4 points) Find the domain of g o h. Write your answer using interval notation. i ,0 = so; : (if; > 7 Km \$2 Thug: Domain 0‘16 551»: [’3] {95ULé’ cu) * .- o :4 't’ l W 3 :It 7 ”73¢? yahé (e) (4 points) Evaluate each of the following. I Z M , 2-. , f(—2) = ‘ﬂrZN/l f(10) = ”[3 ’ 5' (foh)(1) = ¥U H?) = 5:05) 3 1 -’ ( :. vé f [ s .5" (f) (3 points) Is f a one-to—one function? if it is, explain why. if it is not, give a valid reason why not. ¥ {3 Mar (rt. Nofi‘pe,‘ {1(2) : ( Ho) 2: 1 Two difk/MJ Z VA(L¢,»(1 9261A 755% 9m 3 WJM, (4' @MPL‘ Jen/104C ﬁlm/(”15216 ﬁlo»! ‘ﬂx Qaﬁ'ao’t a/QCC ﬂof— 1 > pas; Hm HcaeraNT/K LIME 7547’ Cl/Waziif W""‘é’<‘ ...
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