Math\t107\tSections\t6383\t&\t6390\t-\tQuiz\t#4\t-\tDue\tOctober\t2,\t2016\t-\tpage\t1\tof 5 Follow\tthese\tdirections\tcarefully. This\tquiz\tis\tdue\tby\t11:59\tEastern\ttime\ton\tOctober\t2,\t2016. o This\tis\tan\timportant\tassignment,\tcounting\t12%\tof\tyour\tgrade. o Submit\tthis\tassignment\tin\tyour\tassignments\tfolder\tby\tthe\tdue\tdate. Answer\tall\tthe\tquestions. There\tare\t7\tproblems\ton\t3\tpages. The\tremaining\ttwo pages\thave\textra\tcredit\tproblems. o There\tare\t100\tpoints\tpossible. There\tis\tan\textra\tcredit\tportion\twhere\tyou can\tearn\tan\textra\t20\tpoints. o Show\tall\twork\tin\torder\tto\treceive\tany\tcredit. There\tis\tpartial\tcredit\tfor\tthese problems. Submit\tyour\tassignment\tas\tan\tattachment. Under\tno\tcircumstances\tshould\tyou type\tyour\tanswers\tinto\ta\ttext\tbox. 1. $% & '$ Let\t! " =College Algebra .MATH 107 & % () Fall, 2015, V4.8 5x 2 + 5 21. Let f ( x) = . a. State\tthe\tdomain\tand\twrite\tthe\tanswer\tin\tinterval\tnotation. (4\tpts) x 9 b. State\tthe\tequation\tof\tthe\thorizontal\tasymptote. (2\tpts) (a) State the domain. Answer: _________________ c. State\tthe\tequations\tof\tthe\tvertical\tasymptotes.\t(There\tare\ttwo.) (b) State the horizontal asymptote. Answer: _________________ (4\tpts) 2 $% & '$ (c) State the vertical asymptote(s). Answer: _________________ d. Which\tof\tthe\tfollowing\trepresents\tthe\tgraph\tof ! " = & ? (d) Which of the following represents the graph of f ( x) = 5x 2 + 5 ? x2 9 GRAPH A. GRAPH B. GRAPH C. GRAPH D. % () (2\tpts) Answer: ______________ Page 9 of 11 Math\t107\tSections\t6383\t&\t6390\t-\tQuiz\t#4\t-\tDue\tOctober\t2,\t2016\t-\tpage\t2\tof 5 Fall, 2015, V4.8 Consider\tthe\tpolynomial\t, " ,\tshown\tin\tboth\tstandard\tform\tand\tfactored\tform. 1 9 21 1 shown in 1both standard form and factored form. 20. Consider the polynomial P(x), , " = " 0 " 3 + " 5 + " 15 = " + 1 " 2 " 3 " 5 . College Fall, 2015, V4.8 2 Algebra 2MATH 107 2 2 2 20. Consider the polynomial P(x), shown in both standard form and a. Determine\tthe\tdegree\tof\tthis\tpolynomial. factored\tform. (2\tpts) Which sketch illustrates the end behavior of the polynomial function? b. (a)Which\tsketch\tillustrates\tthe\tend\tbehavior\tof\tthe\tpolynomial\tfunction? College Algebra MATH 107 2. B.end behavior of the polynomial C. function? (a)A. Which sketch illustrates the A. vvvv B. vvvv c. d. e. vvvv C. vvvv D. vvvv vvvv Answer: ________ Answer: ________ the y-intercept. Answer: (b) (b)State y-intercept. Statethe State\tthe\t(", 9)\tcoordinates\tof\tthe\ty-intercept. (c) State the zeros of the function. Answer: (c)State\tthe\tzeros\tof\tthe\tfunction. State the zeros of the function. (d) State which graph below is the graph of P(x). State\twhich\tgraph\tbelow\tis\tthe\tgraph\tof\t, " . (d) State which graph below is the graph of P(x). (2\tpts) Answer: ________________ ________________ (2\tpts) ________________ Answer: ________________ (4\tpts) Answer: ________ (2\tpts) Answer: ________ GRAPH B GRAPH A GRAPH B GRAPH C GRAPH D GRAPH C GRAPH D Write\teach\texpression\tin\tsimplest\t; + <=\tform. Page 8 of 11 a. (1 3=)(8 + 7=) vvvv vvvv GRAPH A 3. D. b. 2 5= 5 (5\tpts) (6\tpts) Page 8 of 11 Math\t107\tSections\t6383\t&\t6390\t-\tQuiz\t#4\t-\tDue\tOctober\t2,\t2016\t-\tpage\t3\tof 5 4. 5. Find\tall\tthe\tsolutions,\treal\tor\tcomplex,\tof\teach\tquadratic\tequation. (Look\tat\tthe\tpoint\tvalues\tto\tsee\twhich\tone\trequires\tmore\twork. Try\tfactoring\tfirst\tif you\tcan. You\tshould\talways\tdo\tthat\tbefore\tjumping\tto\tthe\tquadratic\tformula.) College Algebra MATH 107 Fall, 2015, V4.8 5 a. 6"20. Consider 13" + 6the=polynomial 0 P(x), shown in both standard form and(5\tpts) factored form. b. 4" 5 4" + 17 = 0 (10\tpts) (a) Which sketch illustrates the end behavior of the polynomial function? Which\tsketch\tillustrates\tthe\tend\tbehavior\tof\teach\tpolynomial\tfunction? A. B. vvvv 6. vvvv vvvv y-intercept. (b) State the D. vvvv 5 the function. the3 zeros a. ! (c) " State = 5" 6"of + 2" 1 Solve\teach\tinequality. (5\tpts\teach) Answer: ________________ Answer: ________ (d) State which graph below is the graph of P(x). GRAPH A Answer: ________ Answer: ________________ b. D " = 6" E 3" 5 + 1 GRAPH B (10\tpts\teach) a. " 5 5" 14 < 0 b. 7. C. %(G %'5 0 Consider\tthe\tquadratic\tfunction\t! " = " 5 4" 5. a. Graph\tthis\tfunction. (4\tpts) Answer\teach\tpart.\tYou'll\tneed\tto\tdo\tsome\tof\tthese\tparts\tto\tmake\tthe\tgraph.\t(Parts\tb, f\tand\tg\tshould\tbe\tparticularly\thelpful. Does\tthis\tparabola\topen\tup\tor\tdown?) b. c. d. e. GRAPH C GRAPH D Find\tthe\tvertex. (3\tpts) Find\tthe\tdomain. (2\tpts) Find\tthe\trange. (2\tpts) Find\tthe\tinterval(s)\ton\twhich\tthe\tfunction\tis\tincreasing,\tand\tfind\tthe\tinterval(s) on\twhich\tthe\tfunction\tis\tdecreasing. (4\tpts) f. Find\tthe\t(", 9)\tcoordinates\tof\tthe\tx-intercepts. (4\tpts) g. Find\tthe (", 9)\tcoordinates\tof\tthe\ty-\tintercept. (1\tpt) Math\t107\tSections\t6383\t&\t6390\t-\tQuiz\t#4\t-\tDue\tOctober\t2,\t2016\t-\tpage\t4\tof 5 Extra\tCredit\tProblems. Each\tnumbered\tproblem\tis\tworth\t10\tpoints\ttotal. You\tshould\tuse technology\tto\tdo\tthese. Something\tlike\tExcel\tor\tDesmos\twill\twork\twell. Number\t8\tasks\tfor a\tlinear\tfunction\tof\tthe\tform\t9 = ;" + <,\tand\tNumber\t9\tasks\tfor\ta\tquadratic\tfunction\tof\tthe form\t9 = ;" 5 + <" + I. If\tyou\tgive\ta\tline\tfor\t#9,\tyou\twill\tnot\tget\tany\tcredit\tat\tall\tfor\t#9. 8. Consider\tthe\ttable\tof\tvalues\tgiven\tbelow. Refer\tto\tsection\t2.5,\tstarting\ton\tpage\t225, and\trefer\tto\tExample\t2.5.1. X Y -1 2 -1 3 0 4 1 3 2 7 3 6 4 8 a. Find\tthe\tleast\tsquares\tregression\tline. (5\tpts) b. Give\ta\tverbal\tinterpretation\tof\tthe\tslope\tof\tthe\tline\tof\tbest\tfit. (2\tpts) c. Use\tthe\tregression\tline\tto\tpredict\ty\twhen\tx\tequals\t5. (1\tpts) d. Use\tthe\tregression\tline\tto\tpredict\ty\twhen\tx\tequals\t3. (2\tpts) (Next\tpage\tfor\tNumber\t9.) Math\t107\tSections\t6383\t&\t6390\t-\tQuiz\t#4\t-\tDue\tOctober\t2,\t2016\t-\tpage\t5\tof 5 9. Consider\tthe\ttable\tof\tvalues\tbelow. Refer\tto\tsection\t2.5,\tstarting\ton\tpage\t228, beginning\twith\tthe\tdiscussion\tstarting\tthere\tand\treading\tExample\t2.5.2\ton\tpage\t229. Use\tmilitary\ttimes: for\texample,\t7\tfor\t7am,\tand\t16\tfor\t4pm\t(add\t12\tto\ta\tpm\ttime\tto get\tthe\tmilitary\ttime,\tso\t8pm\tis\t20). Time Temperature in Fahrenheit 7am 35 9am 50 11am 56 1pm 59 2pm 61 4pm 62 8pm 59 11pm 44 a. Fit\ta\tquadratic\tmodel\tfor\tthe\ttemperature\tas\ta\tfunction\tof\ttime,\tand\tcomment\ton the\tgoodness\tof\tfit. (You\tare\tnot\tbeing\tasked\tto\tfit\ta\tlinear\tmodel\there\t-\tyou\tare being\tasked\tfor\ta\tquadratic\tmodel. No\tcredit\tfor\t#9\tunless\tyou\tfit\ta\tquadratic model\tfor\tthese\tquestions. You'll\tneed\ttechnology\tto\tdo\tthis. Excel,\tDesmos,\tor googling\tquadratic\tregression\twill\tget\tyou\tto\ta\tplace\twhere\tyou\tcan\tenter\tthese points\tand\tfit\ta\tmodel.) (5\tpts) b. What\tis\tyour\tpredicted\ttemperature\tat\t3pm? (1\tpts) c. At\twhat\ttime\tof\tday\tdoes\tthe\tmaximum\ttemperature\toccur? (Hint:\tBased\ton\tthe data\tyou're\tgiven,\ta\treasonable\tguess\tis\tthat\tthe\tmaximum\ttemperature\toccurs around\t4pm. The\tactual\tanswer\tis\ta\tlittle\tearlier\tthan\t4pm. Find\tthe\tvertex\tof the\tquadratic\tfunction\tyou\tfound\tin\tpart\t\"a\".) (4\tpts)