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# Review Sheet for MATH 112 at UA

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This 15 page Class Notes was uploaded by an elite notetaker on Friday February 6, 2015. The Class Notes belongs to a course at University of Arizona taught by a professor in Fall. Since its upload, it has received 15 views.

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Date Created: 02/06/15

Answers for Test Review Problems pg 177 210 in Math 112 Workbook 1 i yes each x has exactly one y value ii no Whenx 2 y 5 or2 iii no Whenx 1 y 0 or 2 iv yes each x has exactly one y value 2 C 3 i yes each x has exactly one y value ii yes each x has exactly one y value 4 r 5 1 T ii 1 iii 1 13x 1 5 i 2 ii 0 iii 2x2 iv 0 C 7 i 33 ii M 3 iii 2x2 4x iv 18r2 12r 3 V 6a2 12a 9 8 i Domain x 2 4 Range y 2 225 ii Domain All real numbers 0quot Range y S 3 iii 0 2 0 3 9 D 10 Domain C Range E 11 i Domain xl x 2 2 ii Domain xl x 3x 2 3 12 i Domain all real numbers x 0 Whenx 7 ii Domain all real numbers except m and m x 0 Whenx 0 iii Domain all real numbers x never equals 0 iv Domain x 5 x 0 Whenx i 5 13 C 14 The graph is A 15 E graphs 1 3 and 4 represent functions 16 i C ii T20 325 F After 20 min the temperature in the oven is about 325 F iii At about 10 min iv 375 F 17 i 2200000 ii 455 iii 1001000000 iV decreased 18 i WeightWin ounces CostCin 05 044 10 044 12 061 20 061 24 078 31 095 499 112 19 One possible graph is 20 21 22 23 24 25 26 27 28 time in sec y intercept is the amount of water in the tub before the plug was pulled x intercept is the amount of time it takes the tub to empty ix 4andx 2 ii negative on 42 positive on 200 iii increasing on 00 l decreasing on 400 constant on 14 i neither ii even iii odd iv neither v neither A B i Graph using the window 040 x 040 5 1B 15 23 25 an 35 ii The y intercept 030 is the average cost when producing no plywood iii As x increases the average cost decreases since variable costs generally decrease for large units produced Ax 12x x2 i The area of a circle is a function of the square of the radius ii The volume of a sphere is a function of the cube of the radius iii The area of a square is a function of the square of the side D i IS 500 005S 11 14000 29 i Cx 500 012x n iii x Z 0 iv The y intercept is 0500 This is the basic monthly fee for having the service 30 B 31 i d kt 5400 5k k 1080 d 1080t ii The constant of proportionality is also the slope of the linear function d kt In this problem it represents the speed of sound 123455735 iii d 10808 8640 ft 32 7 meters by 24 meters 33 i The graph of fx le is vertically expanded by 2 and shifted 14 units up 715 710 75 5 10 15 ii The graph of gx x3 is shifted 2 units to the right and vertically compressed by a factor of iii The graph of mx x2 is shifted 23 units to the left re ected across the x axis and shifted down 10 units iV The graph of hx is re ected across the y axis and shifted 56 units up 34 35 36 37 38 39 ifx W ii x x 2 iii fx x3 1 1 706 JC 33 ii 06 363 iii gx x3 2 iV gx x3 2 v goo x3 2 E i iii x 4 74 72 z 4 s 72 74 1 706 fx 5 ii MIC fx 1 2 x x2 1 ii 1 40 41 42 43 44 45 46 47 48 iii x2x2 1 4 1V x212 g V 16 i 350 n 50 1978 iii There were 350000 students majoring in science and engineering in 1978 There were 50000 fewer women than men majoring in science and engineering in i 3 ii No They appear to be unrelated o 7 6 4x 0 1 m f mo 7 x1 g no 2x 5 i Vrt 0 02m2 This gives the volume of the oil slick as a function of time ii about 60 minutes iii It would take about 40 minutes C i 3 ii 1 iii 1 x oo0 or 000 gx oooo g 00 3 or 30 or 02 or 200 gx 00 3 or 32 or 200 i 65 million ii between 1990 and 2013 except at 2000 iii 2000 and 2013 iV between 1990 and 2013 except at 2000 i Yes because there is a constant rate of change between each pair of ordered pairs ii No because the rate of change between pairs of ordered pairs is not constant i Range 070 49 50 51 52 53 54 55 56 57 58 59 60 ii after 1 hour the BAC is 6992 iii between 039 and 205 hours Slope 50 when the price of the product increases by 1 50 fewer items are sold x intercept 0 y intercept 0 i 2 ii 4 iii 3 iv 1 i ii unde ned iii 0 C i y x 1 ii y 1 iii x 2 iv y 4x 5 No The change in y from x 4 to x 5 is 22 The change in y is 21 in the other intervals though the change in x is still 1 Therefore there is no constant slope and the ordered pairs do not lie on a line ifs 4s 250 for s gt 65 ii The slope of the line is 4 The ne increases by 4 for every additional mile per hour over the speed limit iii 90 mph i neither ii perpendicular iii neither iv neither i D ii E A y x 5 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 B First account 180 Second 820 B i Electric C 1100t 5000 Solar C 150t 30000 ii Installation y intercept operation costs year slope iii 263 years The last line is wrong The you are subtracting is multiplied by the 2 in front of the parentheses so you are really subtracting 2 times D i P100 39750 ii P300 250 is the pro t resulting from producing 300 units iii It looks like x 100 units is too low a production level to make a pro t you lose money Producing 300 units helps you recoup the costs Ht t 202 2 i y 53 0x 102 ii 15 feet ifx 1 10x1 102 ii Vertex 1 1013W 1J 0 10 Domain t Z 0 2 100 1 J 0 10 0 x intercepts 29 1000 y intercept 0 iii 55 ft by 110 ft the area is 6050 sq ft y x 52 23 y 4x 22 1 70 trees per acre 98000 apples C 4425 ft 708 ft 58 79 80 81 82 83 84 85 86 87 88 89 90 91 i86 ii28 3x 3x2 3x3 3x4 3x5 i no becausey gt Oasx gt 00 andy gt 0 asx gt 00 ii no because there is a corner or cusp on the graph iii yes because the graph is continuous there are no corners or cusps and y gt 00 as x gt 00 andy gt 00asx gt 00 D i 5 There are 4 turning points ii positive y gt 00 asx gt 00 andy gt 00 asx gt 00 iii negative C 442 9 0 3J29 2 2 B x x 2X96 5x 6 The graph is y 2x 2x 1x 12 i D ii D iii 2 is a zero of multiplicity 3 4 is a zero of mulitplicity 2 one iVThe graph is i 2 ii 3 iii 4 5 is a zero of mulitiplicity 92 B 93 C 94 D 95 157 96 i 3 4 in 97 37 A polynomial function is continuous so in order for it to change from a negative value to a positive value the function must go through zero This happens when the value of x is between 3 and 4 Because f4 is closer to zero than f3 the zero is probably closer to 4 than to 3 thus the guess of a zero at 37 98 D 99 Real zeros 2 15 100 Real solutions 1 2 i J3 101 i They are the same ii They are the same iii The y intercept of g equals 6 times the the y intercept off iv The graph of g is a vertical expansion of the graph off 102 Real zeroes i5 i J2 103 A 104 Real solutions 2 1 i J6 105 x 2x3 5x2 2x 106 D 107 k 25000 b 0986 108 5 109 506 110 i P0 10000 ii P 5 m 8311 iii At the end of 2008 111 56250 lemmings 112 933 years 113 Approximately 27364 hours 114 i 64 ppm ii year 2023 115 i 65 ii about 669 years 116 B 117 pH is 2292 No the lake is acidic 118 i k m 00011995 ii 493 119 i 123114 ii year 2001 120 204892 121 123 124 125 126 127 128 129 130 131 i fx is one to one ii 6 f391x 2 0 3 1 1 2 No The function does not pass the horizontal line test 7 2 D 2 3 12345 x z 4 s a 74 73 21 i shutting down your computer and standing up ii multiply x by 3 then add 5 i 135 9 ii 271320 iii 271320 iv 135 9 if3912 1 ii g391f3 15 4 i g 1 0 386 Kristie Fox the player with batting average 0386 is Kristie Fox ii gf15 0 270 player 15 had batting average 0270 iii f 1 g 1 0408 0 the player with batting average 0408 was player 0 fogx 3 40 3 3 x x 3 3 4x 70006 T L x l 1me X 132 133 134 135 136 137 138 139 140 141 142 143 144 W 4 B i log2433 ii lny a 2 b 05 B 1 2 g 1t 2 log7t i ii Domain oooo Domain oooo Range 0 00 Range 0 00 iii iV Domain oo 00 Range 00 1 y2 1 y 23 iy5 nxlog7429 z 3 115 imn2mzllw C nx m4 ln mx 3 Domain oo 00 Range 0 00 145 ifx 3000011 ii approximately 9 years 146 x 2 147 i 9 ii 9 iii J 3 1V 7 148 vertical asymptote x 2 vertical asymptote x 2 y intercept 0log32 y intercept none x intercepts l0 x intercepts 30 Domain 2oo Domain 200 Range oooo Range 0000 149 i ii y ln x 150 x x gt 13 1 y intercept 0log4l l x intercept 0 151 D 152 i translated 3 units to the left 2 units up ii y ln x 4 iii y lnx 2 153 logb 154 C 155 log510 logsa Zlogsb 1 log52 logsa Zlogsb 155 0 m 11n2 lne 1 ii correct iii correct 157 A 158 i 2629 ii 2569 iii 66686 iv 2153 159 D 160 x 1 161 C 162 x m 21972 163 t 12838 164 y 2 165 i average score of 76 ii average score of 58 iii 55 months after the initial exam 166 X 167 A 168 B 169 f 1x 2 3 1 1 1 k 171 i 220 ladybugs ii The population levels off at 400 ladybugs iii 347 weeks 172 C

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