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# Precalculus I MA 107

NCS

GPA 3.93

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This 21 page Class Notes was uploaded by Braeden Lind on Thursday October 15, 2015. The Class Notes belongs to MA 107 at North Carolina State University taught by Elizabeth Dempster in Fall. Since its upload, it has received 20 views. For similar materials see /class/223694/ma-107-north-carolina-state-university in Mathematics (M) at North Carolina State University.

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Date Created: 10/15/15

Test 2 Material for Math 107 The test will focus on the material since the last test but you need to know all the material from the beginning as it applies to these modules Module 7 Quadratic Functions Module 8 Polynomial Functions Module 9 Rational Functions Module 10 Compositions of Functions Module 11 Inverse Functions Regions bounded by Curves Go over examples from class examples in the moodle try its and the webassign homework problems Here are more practice problems for you to work I ll send answers later 1 N E 4 V39 0 gt1 9 Use the method of completing the square to find the vertex of the following parabola show the completed square form ofthe function 3X2 3X 7 Use the vertex formula method to find the vertex of the following parabola fx 4x2 16x 3 State the range of x2 6x 2 also for this fx find the xvalues in the domain for which the function equals 3 Find the equation for a quadratic function that opens up has vertex 23 and goes through the point l 5 The temperature Tt in degrees Fahrenheit during the day can be modeled by the equation Tt 7t2 94t 593 where t is the number of hours after 600am a At what time is the temperature a maximum round to the nearest minute b What is the maximum temperature Round to the nearest degree A veterinarian uses 600 feet of chainlink fencing to enclose a rectangular region and also subdivide the region into two smaller rectangular regions by placing a fence parallel to one of the sides Find the dimensions that will produce the greatest enclosed area Be sure to draw a figure and label the sides State the degree of the following polynomial state all the zeros and the multiplicity of each What does the multiplicity of the zero tell you about the graph s shape at the particular zero What is the long term behavior of the graph Sketch the graph Px x 52x 23x 4 Follow the same directions in 6 for this function Gx x 43 C2 92 9 Find the horizontal asymptotes of each rational function Ifthere is not a horizontal asymptote just write none 2x3 a x x21 4x32x1 b x g 2x34x26x1 3 4 1 chxw x3 9 Find the vertical asymptotes of each rational function Ifthere is not a vertical asymptote just write none 3 afx x b x g xz x 6 xz x 6 0 Jxw 10 Given the following rational function find its horizontal asymptote and then nd the 2 1 Xvalue where the function crosses this horizontal asymptote hx 2x 2 x x Also for hX fill in the following blanks As x gt 3 the values of hx gt remember that this is read as X approaches 3 from the right hand side As x gt 00 the values of hx gt 11 Given fx 8x 9 and gx m find g o f x and its domain 12 Given the following table of values evaluate the expressions below f o g2gt f 15 g o f1 3 l3 Decom ose the followin function H x so that H x o x p g m f g f X gx Are your answers the only correct ones In other words is that more than one correct way to do this problem 14 Compose these functions and simplify their composition What special relationship exist between these functions 4x and gx 6x 3x f x 6 3x 4 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ony correc f anwwr J04 COWMZ 5 x cf 20f V9x9 44mm fx i fab 1 gm 6X 3x 9 3x4 x 9X gt 31L 900 3 7 3x4 4 3quot 37quot A 3615 6 48 6 3x4 3x 4 3x4 94 97 quot XX 9 quot 8K I 3f2v 9H 31 5mm 4 0 5 4er 10 and am invmm 31M Ca CMQK 30 25 0160 aquot Mm 0M Man MM Lame amd 5 2W One c me S J39Loc 35 am mcrcoohotr 4an Ho fuck 2 mapS I D WA 0L 001ue a and CQCL y go 51 x back 40 o UNCZ yJe x39 Gums quotPM Ro tu A l 0 5439439 6 V0 an6 7390 000 H h Lit o g al ADML 125 arms pa 0 5quot H L39 and 50 Oh no r ko u kl line S 3 A CD W wNG XcP bone 7 Mfg139 Qu rfs Wk Po M4 Rodi l39me 6 V w a a JX Gig f one 39fo ant 4 WAma c4 vw J each American SAW mow quotD fwcPco Sic aa began ack SWOSMEQO Aiamp mapa JIO CL ON bu e AmerMm SiQc QCx J2x5 PXltX392333 I 3 quotZx5 Y sz yguOfcan sec 2 6 65 x SVi39C XL 23 43 3R 3 3QJ 392 7C5 3 3 5 3 J9 rm X th x20 Je39Xy7 4 Ha7i mcho CDmnX3X 5 XZVX L po xaf gt 39 7C 1 7 0 KnotCL If an 7L0 one a f 0391 ammo n 2 K l J x Qfq IxH ampL l 1 W711 5L admit Hy 4 quotxWa q 30 0 ltq17 4 h Jaha A Nocz Inverse 2 JCUAQ Hon W sammwaL 0n 4507 015 A x 31xl 30W 75L a001 7 l 75 1 K 23 7 We 271ng 0 10 uset kon 47676quotO0 x40 K 00 II M 010057 ch 3m 3 x Z 57 X jn rerscc P46 5V39XLZ 0 XLx Sx 0 951 K90 Kq 9 00 MA 111 Supplement Regions Bounded by Curves In calculus nding the area of a region bounded by curves is an important concept Precalculus lays the foundation for this concept by sketching the curves shading the bounded region and by using algebra to determine the points of intersection In the following problems sketch the curves and shade the bounded region Identify the vertices l yx2l and yxl 2 yx2y0xlandx3 3 24y and x2y6 4 y6xx2 and yx2 2x 5 y24x and y2x 4 6 yx and yJc2 7 y3yxandx0 8 yx2 and y 9 y5yandx0 10y2x1 and yx21 llx2y2y xl2xy7 12yx6y 2xyx3 13 x3y l 2xy5 yxl MA 107001 Fall 2010 7 Test 1 Review 7 September a 2010 Justify your answers for each problem 1 Given m 7 xZIZ 713 and 915 a7 79 nd the domain of a V f V The domain of 7 I S w 13 773 U737 77 u 2 Given m 7 I 7 7 nd and simpiify the diffefence quotient i The diffefer ce uo iem is q io h 7 7 m 3 3 Given m 7 2 4 nd and simplify the diffefence quotient a The diffefence uotient is amp q a24aw4 4 Given a function x descfibe tfansfofmations in the Correct ofdef that would yieid the graph ofy2f 73a7s 74 The transformations are 0 Shift fight 8 units 0 Hofizontaiiy compfess by a factor of g o Re ect over the taxis o Vertically stretch b r a factof of2 units 0 Shift down four uni s 5 Given the graph of the function fz beiow detefmine 3 1 a The domain and fange of x The domain oi f ls1l1 The zange off 1s0oo b The intefvais Where x is incieasing decfeasing and constant D O E 6 a o o 1 A w a 9 r 39i J c The ocai maximumminimum vaiues offz ie what is the iocai maxmm The iocai max has vaiue H1 2 The iocai minimum vaiues afe x 7 0 m 7 0 5 and x 7 2 Test 1 Revlew 2z2 lfe3gegl 6 Graph the following plecewlseole neol functlon m 1 lf1lt I g 2 MP2 lfzgt2 7 Trmoblle offers a monthly cell phone plan fol 03999 that lncluoles 350 anytlme mlnutes plus 025 fol each aololltlonal mlnute Flnol the functlon Cz that glves the monthly cell phone blll on this plan Where z is the number of minutes used HOW much would it cost for 400 minutes of Lalkrtime7 39 99 MOST 3350 01 V 39 99 0 25z 73507 If e gt 350 Fox 400 nnnutes of talk tune ll would costC400 52 49 e tempelatule T of the all ls apploxlrnately a linear functlon of the altltuole h for altltuoles wlthln 10000 metels of the surface of the Earth If the surface tempelatule ls 30 C and the tempelatule at 1000 metels ls 5 C nd the functlon T T01 701102511 30 lven a functl n x wnte the formula of the functlon tz obtalneol altel shlft 3 unlts then lellectlng across the or ctlon ls 2a if g 10 Conslolel the functlon mg m light axis then horizontally stletchlng by a factol of 5 3 7c1 7z2 m o Is the polnt 19 on the graph of f The polnt 15 ls not on the glaph of f l a 2 what ls x What polnt ls on the graph of f7 3 so the polnt 2 g ls on the glaph of f o If z 72 what ls fz7 What polnt ls on the graph of f t sthe olornaln of f The clolnaln of f ls 70o e2 Ule2oo 11 n open box wlth a square base ls to be maole from a square plece of cardboard 24 lnches on a slde by cuttlng out a square wlth slde length a from each Come and tulnlng up the sloles 2 Test 1 Review 0 Express the volume V of the box as a function of the length x of the side of the square cut from each corner 2024 7 2z2 0 What is the volume if a 3 inch square is cut out V3 972 cubic inches 0 What is the volume if a 10 inch square is cut out V10 160 cubic inches 12 Determine algebraically if the following functions are even7 odd or neither 0 f 4mg This function is odd 0 990 m M This function is neither odd nor even hlttgt 7 i 7 3m2 7 9 This function is even 13 What is the domain of the following functions 0 4mg The domain is R 0 995 m lml The domain is R 1 39 W m The domain is 7007 U 7x3 U 00 14 State the domain7 range7 any z and y intercepts7 intervals where the function is increas ingdecreasingconstant7 and local maxima and minima for the following functions o ft t3 2 7 Domain R Range R 7 z intercept O y intercept 02 7 Increasing on entire domain Decreasing nowhere Constant nowhere 7 No lolcal max or min 0 996 m 7 2 7 Domain IR 7 Range R 7 7 z intercept None y intercept 07 7 Increasing nowhere Decreasing on entire domain Constant nowhere 7 No local max or min h l2873l A Va V 7 Domain R Range 07 7 z intercept 370 y intercept 03 7 Increasing on 00 Decreasing on 7007 Constant nowhere 7 No local max Local min occurs at s with value hs 0 3 More Practice with Exponential and Logarithmic materials 1 The number N of bacteria present in a culture at time t in mins obeys the function N I 50 39 20 a Determine the number of bacteria at t 0 mins b What is the population after 20 mins 0 When will the number of bacteria reach 400 2 Graph the following exponential function 37K 2 clearly show and state the applicable asymptote Also state the following a State the domain b State the yintercept c Find the XValue of the point on the graph where the yValue is 7 3Graph the following logarithmic function gx log2x 2 clearly show and state any applicable asymptote Also state the following State the domain e State yintercept f Find the XValue of the point on the graph where the yValue is 3 4 Solve the following equations 1 xlo a g232 b 2quot2391 8 c 2quot 10 d 565 45 e 2 2 2 32 0 f 10g43x 210g4x g ezx 4ex30 h10g2 x log2x 7 3 j 210g3x 4 log392 k log2x 6 log2x 4 log2 x 2 5 Medical research indicates that the risk of having a car accident increases exponentially as the concentration of alcohol in the blood increases The risk is modeled by R 6 6127 where X is the blood alcohol concentration and R given as a percent is the risk of having a car accident What blood alcohol concentration corresponds to a 17 risk of a car accident 6 nswers 0 5 Mia h Jmee 3 N 50QIt D Gwm Jaws15L 0 Moj 0 9f ream dammit W is E aoj 50 ampI20 U A 0 M o a 9 00 bntcriqd artt ampIt 9 3 aJt 3 I 30 f chzhw s0 9 n39 Hak u rkS ov xO39II Wc UH S lm39 3 quot HY X l39 63 ran MAW QHd alum limb I 0 X14 2 3 JAQY nIO 7 31082x X Lf Una 1no 3J03L7 93 Jn10 f Van94 3 a 53345 a X xa 9 1 39O X 5X me 6 i 9 1M5quot an 191 919 32 0 575 am G39 49quot 3ao LWQM 470 9180 x C39OfY39Hnueng Jawa Jo q 37 s 2 10941 2x4 3 0 194437 294651 3equot 00 376 x aft30 equot l 0 0 xrsx 333 6 0 1 76 37 I 10 106 Jlng Qne 0r 9 ng gx 4 Jogzx jogzKIC7 3 Q alogfa 105139 9 10 xyvt 3 Jog 78 10339 6L X 91 aimH 10917 0 2cz 7xv l 3 757 0 X39Xl C sit Hf 75 9 L Na m doma39m 91 ampq J yz 6gt10 0z7C Lf glx sad 9 7glf JDzX oxmgt 3 4 9 x g 2 5 B 76 079 043wa 31mg 2 m LxX39 xLD W 66 7 1K 5 XZngHQL A 8quot x O 5XL 4 24 Jn inalzwx a a 0 x mix Jnm 7x Ci ELLEs 5 L93 07z M 3e Q Rm W boa Wk Pmb CMiT gu 39 00fo f3 Jlogt KProbuem 0 30315 0820 WJM 5 Jog 00ng wwwoit 39 O 0301 5100 7b 5 0 109x 103x I 5 10976 0 10376 5 3 3L Mc 0 M a mquot x 05 x M WWW s 4 09000 x Factoring Supplemental Worksheet MAID Transcribed by Megan Sawyer August 18 2010 Instructions Simplify each problem below by factoring H E0 r U 2x 16z 3x2 7 22 6031 7 3x2554 7 12 7 30x5x4 7131 7 3x24 3Q 712z 24 4Q 713z 2 2 1z 7 I 7 2 12z 7 1 3 6x2 3x 12 32 6x2 3x 12 817 322 713 62x 7 1417 3x 1 7 3w x 7 121 7 2m 7 22 z 7 2 71 95 i 14 x 7 13 7 3m 7 5 7 12 95 i 06 Answers H E0 U 03 5 23z 23x i 1 30z5z4 71217 3x241 2x2 711954 x 712z 237x 2 7495 1 96 7 13 22x 7 131 7 6x 1 7 3amp3 z 7 5 95 i 13 27 7 95 i 14

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