ALL multiple choice, only need to pick 1 from each question.
Jungshik Shin F2021UPG101-093 Final Exam is due on Tuesday, December 07, 2021 at 12:00pm. The number of attempts available for each question is noted beside the question. If you are having trouble figuring out your error, you should consult the textbook, or ask a fellow student, one of the TA’s or your professor for help. There are also other resources at your disposal, such as the Mathematics Continuous Tutorials. Don’t spend a lot of time guessing – it’s not very efficient or effective. Make sure to give lots of significant digits for (floating point) numerical answers. For most problems when entering numerical answers, you can if you wish enter elementary expressions such as 2∧ 3 instead of 8, sin(3 ∗ pi/2)instead of -1, e∧ (ln(2)) instead of 2, (2+ tan(3))∗ (4− sin(5))∧6−7/8 instead of 27620.3413, etc. Problem 1. (1 point) Which of the following graphs represents a relationship where y is a function of x? Note: You can click on the graph for a larger view. • A • B • C • D • E • F Answer(s) submitted: • (incorrect) 1 Problem 2. (1 point) In the following graph, y = f (x) is illustrated in blue and y = g(x) is illustrated in green. Evaluate ( f −g)(0). • −1 • 0 • 1 • 2 • 3 • 4 Answer(s) submitted: • (incorrect) Problem 3. (1 point) f (x) = x3−9x2 +27x−21. The inverse function is f−1(x) = . . . • 3 √ x+6−3 • −1x3−9x2+27x−21 • 3 √ x−6+3 • 3 √ x−6−3 • 1x3−9x2+27x−21 • 3 √ x+6+3 Answer(s) submitted: • (incorrect) 2 Problem 4. (1 point) f (x) = 2x−3 if x≤ 0 1 if 0 < x="">< 3="" x2="" +3="" if="" x≥="" 3="" .="" evaluate="" f="" (3).="" •="" −3,1,12="" •="" −3,1="" •="" −3="" •="" 1="" •="" 1,12="" •="" 12="" answer(s)="" submitted:="" •="" (incorrect)="" problem="" 5.="" (1="" point)="" consider="" the="" point="" p="(−10,0)" on="" the="" graph="" of="" y="f" (x).="" find="" the="" point="" corresponding="" to="" p="" on="" the="" graph="" of="" y="−5" f="" (="" 2(x+="" 4)="" )="" −2.="" •="" (−4,−2)="" •="" (−4,48)="" •="" (−9,48)="" •="" (−10,48)="" •="" (−10,−2)="" •="" (−9,−2)="" answer(s)="" submitted:="" •="" (incorrect)="" problem="" 6.="" (1="" point)="" the="" function="" y="f" (x)="" illustrated="" below="" has="" neither="" even="" nor="" odd="" symmetry.="" determine="" which="" of="" the="" following="" shifted="" functions="" of="" f="" has="" odd="" symmetry.="" •="" f="" (x+3)+1="" •="" f="" (x+5)+1="" •="" f="" (x+1)−6="" •="" f="" (x+5)−6="" •="" f="" (x+1)+8="" •="" f="" (x+3)+8="" answer(s)="" submitted:="" •="" (incorrect)="" 3="" problem="" 7.="" (1="" point)="" determine="" the="" equation="" of="" the="" ellipse="" that="" is="" illustrated="" in="" the="" graph="" below.="" •="" (x−1)="" 2="" 6="" +="" (y+2)2="" 2="1" •="" (x−1)="" 2="" 4="" +="" (y+2)2="" 36="1" •="" (x−1)="" 2="" 36="" +="" (y−2)2="" 4="1" •="" (x−1)="" 2="" 2="" +="" (y+2)2="" 6="1" •="" (x−1)="" 2="" 4="" +="" (y−2)2="" 36="1" •="" (x−1)="" 2="" 36="" +="" (y+2)2="" 4="1" answer(s)="" submitted:="" •="" (incorrect)="" problem="" 8.="" (1="" point)="" consider="" the="" function="" f="" (x)="16x8" +bx6="" +4="" 4x6="" +="" cx5="" +4="" where="" b="" and="" c="" are="" real="" numbers.="" if="" you="" set="" up="" long="" division,="" what="" is="" the="" first="" term="" a="" across="" the="" top?="" •="" a="4x" •="" a="16x2" •="" a="64x14" •="" a="16x3" •="" a="1" •="" a="4x2" answer(s)="" submitted:="" •="" (incorrect)="" problem="" 9.="" (1="" point)="" f="" (x)="15x4" +ax3="" +bx2="" +cx+25,="" where="" a,b,c="" are="" integers.="" the="" list="" of="" all="" potential="" rational="" zeroes="" of="" f="" (x)="" is:="" •="" ±{1,3,5,15,="" 15="" ,="" 3="" 5="" ,="" 1="" 25="" ,="" 3="" 25}="" •="" ±{1,5,25,="" 15="" ,="" 1="" 3="" ,="" 5="" 3="" ,="" 25="" 3="" ,="" 1="" 15}="" •="" ±{1,5,25}="" •="" ±{1,3,5,15,25}="" •="" ±{1,3,5,15}="" •="" ±{1,5,25,="" 15="" ,="" 1="" 3="" ,="" 1="" 15}="" answer(s)="" submitted:="" •="" (incorrect)="" 4="" problem="" 10.="" (1="" point)="" consider="" the="" following="" set:="" (−∞,−4)∪="" (1,3)∪="" (3,∞).="" which="" of="" the="" following="" inequalities="" has="" this="" set="" as="" its="" solution?="" •="" (x+4)5(x−1)5(x−3)3=""> 0 • (x+4)6(x−1)4(x−3)7 > 0 • (x+4)5(x−1)5(x−3)2 > 0 • (x+4)3(x−1)4(x−3)4 > 0 • (x+4)4(x−1)2(x−3)6 > 0 • (x+4)7(x−1)4(x−3)5 > 0 Answer(s) submitted: • (incorrect) Problem 11. (1 point) Suppose that a<>< c.="" the="" graph="" of="" y="f" (x)="" is="" illustrated="" below.="" which="" of="" the="" following="" functions="" best="" describes="" f="" (x)?="" •="" f="" (x)="(x−a)2(x−b)(x−" c)="" •="" f="" (x)="(x−a)(x−b)2(x−" c)="" •="" f="" (x)="(x−a)(x−b)(x−" c)2="" •="" f="" (x)="(x−a)2(x−b)2(x−" c)="" •="" f="" (x)="(x−a)2(x−b)(x−" c)2="" •="" f="" (x)="(x−a)(x−b)2(x−" c)2="" answer(s)="" submitted:="" •="" (incorrect)="" 5="" problem="" 12.="" (1="" point)="" consider="" the="" rational="" function="" f="" (x)="x" 2+ax+b="" x2+cx+d="" .="" suppose="" that="" the="" graph="" y="f" (x)="" has="" zeroes="" at="" x="−1" and="" x="6" and="" vertical="" asymptotes="" at="" x="−2" and="" x="5." find="" the="" y-intercept.="" •="" f="" (0)="65" •="" f="" (0)="−6" •="" f="" (0)="−10" •="" f="" (0)="53" •="" f="" (0)="35" •="" f="" (0)="12" answer(s)="" submitted:="" •="" (incorrect)="" problem="" 13.="" (1="" point)="" simplify="" the="" following:="" (="" 3x4y5="" )4="" •="" 81x8y9="" •="" 81x16y20="" •="" 12x8y9="" •="" 12x16y20="" •="" 12x256y625="" •="" 81x256y625="" answer(s)="" submitted:="" •="" (incorrect)="" problem="" 14.="" (1="" point)="" the="" following="" graph="" represents="" an="" exponential="" function="" of="" the="" form="" f="" (x)="Aebx" +="" k.="" what="" is="" the="" value="" of="" k?="" •="" k="−3" •="" k="−2" •="" k="−1" •="" k="1" •="" k="2" •="" k="3" answer(s)="" submitted:="" •="" (incorrect)="" problem="" 15.="" (1="" point)="" find="" the="" domain="" of="" the="" following="" logarithmic="" function:="" f="" (x)="log9(4−9x)." •="" x=""> 4 • x < 49="" •="" x=""> 49 • x < 0="" •="" x=""> 0 • x < 4 answer(s) submitted: • (incorrect) 6 problem 16. (1 point) expand and simplify the following logarithm: log2 ( 32(a+1)5 b4c4 ) • 32+5log2(a+1)−4log2 b−4log2 c • 5+5log2(a+1)−4log2 b+4log2 c • 32+5log2(a+1)−4log2 b+4log2 c • 16+5log2(a+1)−4log2 b−4log2 c • 16+5log2(a+1)−4log2 b+4log2 c • 5+5log2(a+1)−4log2 b−4log2 c answer(s) submitted: • (incorrect) problem 17. (1 point) consider the following logarithmic equation: log2(x+4)+ log2(x+8) = 5. when solving the equation, which of the following would be equivalent: • (x+4)+(x+8) = 10 • (x+4)(x+8) = 25 • (x+4)+(x+8) = 25 • (x+4)+(x+8) = 32 • (x+4)(x+8) = 32 • (x+4)(x+8) = 10 answer(s) submitted: • (incorrect) problem 18. (1 point) a radioactive substance initially has a mass of 820 grams. after 9 seconds, the mass has reduced to 664 grams. assuming exponential decay, we can model the mass (in grams) of the substance after t seconds by m(t) = . . . • 820e−0.07688t • 820e0.02345t • 820e0.07688t • 820e−0.02345t • 820e−0.21102t • 820e0.21102t answer(s) submitted: • (incorrect) 7 problem 19. (1 point) find the measure of angle a, to the nearest tenth. • a = 57.1◦ • a = 32.9◦ • a = 40.4◦ • a = 49.6◦ • a = 122.9◦ • a = 139.6◦ answer(s) submitted: • (incorrect) problem 20. (1 point) sin(a) = −17819469 . if a is in quadrant 4, find the exact value of tan(a): • −93009469 • −3832000 • −17819300 • 17819300 • 93009469 • 3832000 answer(s) submitted: • (incorrect) problem 21. (1 point) consider the graph of the function f (x) = 16sin(bx + c) + 17, where b and c are real constants. what is the range of y = f (x)? in other words, what is the set of possible y-values? • (−1,33) • [0,16] • [−1,33] • [1,33] • (0,16) • (1,33) answer(s) submitted: • (incorrect) problem 22. (1 point) find the length of the side x in the following illustration, correct to two decimal places: note that the illustration is “mostly” to scale and there are no in- dicated right-angles. • x = 60.24 • x = 76.26 • x = 43.59 • x = 32.99 • x = 73.19 • x = 41.07 answer(s) submitted: • (incorrect) 8 problem 23. (1 point) the graph of a trigonometric function y = f (x) is illustrated in blue below: using the graph, find all solutions in r to f (x) = 4. • x = 2+2k,4+2k for all k in z • x = 4+5k for all k in z • x = 2+3.5k for all k in z • x = 2+5k,4+5k for all k in z • x = 2+2k for all k in z • x = 2+7k,4+7k for all k in z answer(s) submitted: • (incorrect) problem 24. (1 point) evaluate arccos ( − √ 3 2 ) in degrees. • a =−60◦ • a =−45◦ • a =−30◦ • a = 120◦ • a = 135◦ • a = 150◦ answer(s) submitted: • (incorrect) problem 25. (1 point) consider the trigometric expression: 1−sin(x)cos(x) . using trigonometric identities, this expression is equivalent to: • sin(x) tan(x) • sec2(x) • sin(x)− cos(x) • sec(x)− tan(x) • 1−cos(x)sin(x) • cos2(x) answer(s) submitted: • (incorrect) problem 26. (1 point) angles a and b are both in the first quadrant (in the interval [0, π2 )). given sin(a) = 144145 and tan(b) = 8 15 , evaluate cos(a−b). • 14082465 • 14072465 • −8972465 • 14062465 • −8962465 • −8982465 answer(s) submitted: • (incorrect) 9 problem 27. (1 point) evaluate the following: 108!105! . • 128618280 • 1259712 • 11664 • 11340 • 11556 • 1224936 answer(s) submitted: • (incorrect) problem 28. (1 point) jeremiah wants to decorate his laptop with a row of stickers across the top. he has 11 distinct stickers to choose from for this task. his favourite numbers are 2 and 6 so he will decorate his laptop with a row of with either 2 or 6 stickers. how many different ways could he arrange the stickers? • 36590400 • 332640 • 332750 • 517 • 110 • 6652800 answer(s) submitted: • (incorrect) problem 29. (1 point) brent’s restaurant sells poke bowls. in a mega-bowl, you can choose • a base of either spinach or rice • 2 different proteins of either tuna, salmon, scallop, tofu, or chicken • 2 different fillers from a selection of 6 • 4 different toppings from a selection of 6 how many different mega-bowls of poke can you make? • 432000 • 19 • 412 • 42 • 4500 • 360 answer(s) submitted: • (incorrect) problem 30. (1 point) in the expanded and simplified expression of f (x) = (3x4−5)14, find the x44 term. • 8060188500x44 • −177147x44 • −8060188500x44 • 479882812500x44 • −479882812500x44 • 177147x44 answer(s) submitted: • (incorrect) generated by c©webwork, http://webwork.maa.org, mathematical association of america 10 jungshik shin f2021upg101-093 final exam is due on tuesday, december 07, 2021 at 12:00pm. the number of attempts available for each question is noted beside the question. if you are having trouble figuring out your error, you should consult the textbook, or ask a fellow student, one of 4="" answer(s)="" submitted:="" •="" (incorrect)="" 6="" problem="" 16.="" (1="" point)="" expand="" and="" simplify="" the="" following="" logarithm:="" log2="" (="" 32(a+1)5="" b4c4="" )="" •="" 32+5log2(a+1)−4log2="" b−4log2="" c="" •="" 5+5log2(a+1)−4log2="" b+4log2="" c="" •="" 32+5log2(a+1)−4log2="" b+4log2="" c="" •="" 16+5log2(a+1)−4log2="" b−4log2="" c="" •="" 16+5log2(a+1)−4log2="" b+4log2="" c="" •="" 5+5log2(a+1)−4log2="" b−4log2="" c="" answer(s)="" submitted:="" •="" (incorrect)="" problem="" 17.="" (1="" point)="" consider="" the="" following="" logarithmic="" equation:="" log2(x+4)+="" log2(x+8)="5." when="" solving="" the="" equation,="" which="" of="" the="" following="" would="" be="" equivalent:="" •="" (x+4)+(x+8)="10" •="" (x+4)(x+8)="25" •="" (x+4)+(x+8)="25" •="" (x+4)+(x+8)="32" •="" (x+4)(x+8)="32" •="" (x+4)(x+8)="10" answer(s)="" submitted:="" •="" (incorrect)="" problem="" 18.="" (1="" point)="" a="" radioactive="" substance="" initially="" has="" a="" mass="" of="" 820="" grams.="" after="" 9="" seconds,="" the="" mass="" has="" reduced="" to="" 664="" grams.="" assuming="" exponential="" decay,="" we="" can="" model="" the="" mass="" (in="" grams)="" of="" the="" substance="" after="" t="" seconds="" by="" m(t)="." .="" .="" •="" 820e−0.07688t="" •="" 820e0.02345t="" •="" 820e0.07688t="" •="" 820e−0.02345t="" •="" 820e−0.21102t="" •="" 820e0.21102t="" answer(s)="" submitted:="" •="" (incorrect)="" 7="" problem="" 19.="" (1="" point)="" find="" the="" measure="" of="" angle="" a,="" to="" the="" nearest="" tenth.="" •="" a="57.1◦" •="" a="32.9◦" •="" a="40.4◦" •="" a="49.6◦" •="" a="122.9◦" •="" a="139.6◦" answer(s)="" submitted:="" •="" (incorrect)="" problem="" 20.="" (1="" point)="" sin(a)="−17819469" .="" if="" a="" is="" in="" quadrant="" 4,="" find="" the="" exact="" value="" of="" tan(a):="" •="" −93009469="" •="" −3832000="" •="" −17819300="" •="" 17819300="" •="" 93009469="" •="" 3832000="" answer(s)="" submitted:="" •="" (incorrect)="" problem="" 21.="" (1="" point)="" consider="" the="" graph="" of="" the="" function="" f="" (x)="16sin(bx" +="" c)="" +="" 17,="" where="" b="" and="" c="" are="" real="" constants.="" what="" is="" the="" range="" of="" y="f" (x)?="" in="" other="" words,="" what="" is="" the="" set="" of="" possible="" y-values?="" •="" (−1,33)="" •="" [0,16]="" •="" [−1,33]="" •="" [1,33]="" •="" (0,16)="" •="" (1,33)="" answer(s)="" submitted:="" •="" (incorrect)="" problem="" 22.="" (1="" point)="" find="" the="" length="" of="" the="" side="" x="" in="" the="" following="" illustration,="" correct="" to="" two="" decimal="" places:="" note="" that="" the="" illustration="" is="" “mostly”="" to="" scale="" and="" there="" are="" no="" in-="" dicated="" right-angles.="" •="" x="60.24" •="" x="76.26" •="" x="43.59" •="" x="32.99" •="" x="73.19" •="" x="41.07" answer(s)="" submitted:="" •="" (incorrect)="" 8="" problem="" 23.="" (1="" point)="" the="" graph="" of="" a="" trigonometric="" function="" y="f" (x)="" is="" illustrated="" in="" blue="" below:="" using="" the="" graph,="" find="" all="" solutions="" in="" r="" to="" f="" (x)="4." •="" x="2+2k,4+2k" for="" all="" k="" in="" z="" •="" x="4+5k" for="" all="" k="" in="" z="" •="" x="2+3.5k" for="" all="" k="" in="" z="" •="" x="2+5k,4+5k" for="" all="" k="" in="" z="" •="" x="2+2k" for="" all="" k="" in="" z="" •="" x="2+7k,4+7k" for="" all="" k="" in="" z="" answer(s)="" submitted:="" •="" (incorrect)="" problem="" 24.="" (1="" point)="" evaluate="" arccos="" (="" −="" √="" 3="" 2="" )="" in="" degrees.="" •="" a="−60◦" •="" a="−45◦" •="" a="−30◦" •="" a="120◦" •="" a="135◦" •="" a="150◦" answer(s)="" submitted:="" •="" (incorrect)="" problem="" 25.="" (1="" point)="" consider="" the="" trigometric="" expression:="" 1−sin(x)cos(x)="" .="" using="" trigonometric="" identities,="" this="" expression="" is="" equivalent="" to:="" •="" sin(x)="" tan(x)="" •="" sec2(x)="" •="" sin(x)−="" cos(x)="" •="" sec(x)−="" tan(x)="" •="" 1−cos(x)sin(x)="" •="" cos2(x)="" answer(s)="" submitted:="" •="" (incorrect)="" problem="" 26.="" (1="" point)="" angles="" a="" and="" b="" are="" both="" in="" the="" first="" quadrant="" (in="" the="" interval="" [0,="" π2="" )).="" given="" sin(a)="144145" and="" tan(b)="8" 15="" ,="" evaluate="" cos(a−b).="" •="" 14082465="" •="" 14072465="" •="" −8972465="" •="" 14062465="" •="" −8962465="" •="" −8982465="" answer(s)="" submitted:="" •="" (incorrect)="" 9="" problem="" 27.="" (1="" point)="" evaluate="" the="" following:="" 108!105!="" .="" •="" 128618280="" •="" 1259712="" •="" 11664="" •="" 11340="" •="" 11556="" •="" 1224936="" answer(s)="" submitted:="" •="" (incorrect)="" problem="" 28.="" (1="" point)="" jeremiah="" wants="" to="" decorate="" his="" laptop="" with="" a="" row="" of="" stickers="" across="" the="" top.="" he="" has="" 11="" distinct="" stickers="" to="" choose="" from="" for="" this="" task.="" his="" favourite="" numbers="" are="" 2="" and="" 6="" so="" he="" will="" decorate="" his="" laptop="" with="" a="" row="" of="" with="" either="" 2="" or="" 6="" stickers.="" how="" many="" different="" ways="" could="" he="" arrange="" the="" stickers?="" •="" 36590400="" •="" 332640="" •="" 332750="" •="" 517="" •="" 110="" •="" 6652800="" answer(s)="" submitted:="" •="" (incorrect)="" problem="" 29.="" (1="" point)="" brent’s="" restaurant="" sells="" poke="" bowls.="" in="" a="" mega-bowl,="" you="" can="" choose="" •="" a="" base="" of="" either="" spinach="" or="" rice="" •="" 2="" different="" proteins="" of="" either="" tuna,="" salmon,="" scallop,="" tofu,="" or="" chicken="" •="" 2="" different="" fillers="" from="" a="" selection="" of="" 6="" •="" 4="" different="" toppings="" from="" a="" selection="" of="" 6="" how="" many="" different="" mega-bowls="" of="" poke="" can="" you="" make?="" •="" 432000="" •="" 19="" •="" 412="" •="" 42="" •="" 4500="" •="" 360="" answer(s)="" submitted:="" •="" (incorrect)="" problem="" 30.="" (1="" point)="" in="" the="" expanded="" and="" simplified="" expression="" of="" f="" (x)="(3x4−5)14," find="" the="" x44="" term.="" •="" 8060188500x44="" •="" −177147x44="" •="" −8060188500x44="" •="" 479882812500x44="" •="" −479882812500x44="" •="" 177147x44="" answer(s)="" submitted:="" •="" (incorrect)="" generated="" by="" c©webwork,="" http://webwork.maa.org,="" mathematical="" association="" of="" america="" 10="" jungshik="" shin="" f2021upg101-093="" final="" exam="" is="" due="" on="" tuesday,="" december="" 07,="" 2021="" at="" 12:00pm.="" the="" number="" of="" attempts="" available="" for="" each="" question="" is="" noted="" beside="" the="" question.="" if="" you="" are="" having="" trouble="" figuring="" out="" your="" error,="" you="" should="" consult="" the="" textbook,="" or="" ask="" a="" fellow="" student,="" one="">