{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

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

Info icon This preview shows pages 1–6. Sign up to view the full content.

View Full Document Right Arrow Icon
Image of page 1

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 2
Image of page 3

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 4
Image of page 5

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 6
This is the end of the preview. Sign up to access the rest of the document.

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’<‘ ...
View Full Document

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern