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# PRECALCULUS ALGEBRA MAC 1140

UF

GPA 3.8

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This 8 page Class Notes was uploaded by Marquise Graham on Saturday September 19, 2015. The Class Notes belongs to MAC 1140 at University of Florida taught by Kwai-Lee Chui in Fall. Since its upload, it has received 14 views. For similar materials see /class/207046/mac-1140-university-of-florida in Calculus and Pre Calculus at University of Florida.

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Date Created: 09/19/15

MAC1140 Review 11 Lectures 8sec0nd half L15 Rules for the Inverses L12 a f 1fx x for all x in the domain of f b Domain of f 391 Range of f f Ky y for all x in the domain of f Range of f 1 Domain of f Equivalently x y lt3 16710 x c The graph of f and f 1 are re ections of each other across the line y x fx2fx1 A Average rate of change of f from x1 to x2 1 62 x1 x2 x1 Ax The vertex ofthe parabola fxax2 bx c is hk where hiband kfh a Complexnumber 2392 l V a 61 agt0 1393 z39 1394 1 The remainder Theorem Iffx x kqx r then r The factor Theorem A polynomial has a factor x k if and only if 0 Also know Parent functions mentioned in lectures and their graphs Composite functions and how to find its domain Leading coefficient Test and zeros and their multiplicities to help graphing polynomials You can nd all the above information in lecture outlines or in the text book 1 L14 Match the graph with its polynomial function y 1 4 1 9 1 9 a 2x373xl 77x3x277 c 7x572x37x d 77x572x37x b 3 3 5 5 5 5 2 L14 Given the graph below is it an even or oddpolynomial Is the leading coef cient an positive or negative Constru ct a possible polynomial that matches the graph and the given points the answer is not unique 1 3 L14 Sketch hx ilxx 7 42 determine the end behavior and intercepts zeros and multiplicities 4 L14 Sketch fx 75x2 7 x3 how many turning points does the graph have 5 L13 A ball was thrown upward with initial velocity 80 sec from a bridge ofheight 96 it above ariver A er t seconds its height above the ground is given by ho 71612 801 96 a What is the maximum height of the ball b When does the ball reach that height c At what time will the ball fall into the river d Find all intercepts of the graph of the equation e Sketch the graph and label all important point 6 L13 The demand function for a sofa at a furniture outlet has been deterrninedto be p agar 1100 where p is the price ofa sofa The cost functionis a xed cost of 7500 plus 500 per unit a Find the pro t function 131 b Find the production level that will maximize pro t c What price will maximize the pro t on the graph 7 L14 Find all zeros ofg 21393 9x x 3 3x2 43 and their multiplicities and determine if graph touches or cross at the zeros also nd the intercepts and end behavior 8 L13 Find the equation of the parabola that has vertex 34 and passing through the point 12 9 L13 a Find the vertex and the range ofthe parabola 7x2 4x 1 ll ii r 10 L14 Use synthetic division to show that Xl and X2 are factors of fX 2x4 3x3 4x2 3x 2 and factor fX completely 11 L15 a Find the conjugate zofthe following then nd 2 z z z z z z z for a i z 2 396 ii 2 3i iii 2 5 b Evaluate i 2i 662i ii 12 75 iii 12 x 75 iv x 12 12 L15 Perform the indicated operations Write your answer in standard form a 43i43i b i23 12 0 i3 13 L10 Consider the equation y lx1l a The point 21 lies on the graph of the equation TF b Find the X and y intercepts c What kind of symmetry does the graph have 14 L9 Let f be a function such that the point 35 lies on its graph Find f3 if a f is even b f is odd 15 L9 Find the average rate of change offX from X 3 to X 1 l x 16 L9 Which of the following equations is w a fx b fx c fx x3 x d fx lxl e Vquot f x2 i 1 17 L10 Consider the graph of a function Identify the parent function 7 Vertical shift 7 units up down select one 7 Horizontal shift 7 units right left select one 7 Re ection across X y aXis select one 7 Vertical compression stretch select one Construct the function using the given points 1 18 L12 Given a onetoone function x 2 Find f1 and the range of f x 19 L1 1 Let g V39ix39 16 and f be an even function such that the point 35 lies on the graph of f Find a Lg fJ 3 b fag 20 L11 Let fx x2 1 gx J Find f o gx and nd the domain ofthis composite function 21 Which of the following equation is 1 shown in this graph l l 1 1 ay71 by71 cy x1 x1 1 ey 7 1 X 1 23 a Ifgx is a onetoone function and 1 bj is a point on its graph then 9 1 b b If hx is odd and ab is a point on its graph what s M a c What s 901 aD Partial Answer Review Unit II 1 c 5zeros n 2 5 n is odd and a gt 0 4 turns again n 2 5 2 even an gt0 zeros 4odd multiplicity 0 even multiplicity 4odd multiplicity y x2x 4x4 3 degree 3 odd an lt 0 end behavior rises to the left and falls to the right turning points S 2 x int 004 0 y int 00 zeros 0odd mult 4even mult 4 degree 3 odd an lt 0 end behavior rises to the left and falls to the right turning points S 2 x int 50x y int 00 zeros 5odd multiplicity 0even mult 5 a and b maximum height occurs when t25 and is h25196feet c Att 6 seconds d 10 6 0 0 96 e parabola opens down with vertex at 25 196 and intercepts at those points listed in d 25 6a Revenue is Rx px jx2 1100x cost is Cx 7500 500139 Profit Px GOBx 7500 b 48 units c 800 7zeros 0 multiplicity lcross 3 multiplicity 4t0uch 3 multiplicity lcross yint y0 rises on both sides s y x32 4 9a vertex24 R oo4 is 10x1x 22x1x1 11a 1 245 13903 m5 azz 4 z z 2kg 2 9 22 L93i bi2139E iv 30 nu 315 iv 30139 12 a 6i b 2139 c 41 d 1i 13 a T b y int 01 x int 0 c none 14 a 5 b 5 15 18 16 c 17 vertical shift 1 units down horizontal shift 3 units to the right vertical stretch y 1471x 32 l 18 f lRf Df oolUlOO 19 a 3 b 5 note Sincefis even f3f 3 20 o gx x1 D0 oo 21 d 22 H E0 00 4 U 03 5 00 a Simplify the complex fraction MAC 1140 Test I Review Fall 2010 Sections R6 Complex Fractions 18 Absolute Value Equations 32 7 2 1 7 42 2 1 2amp2 7 4 1 x 725 125 23 12 4 b Evaluate the expression 025 39 7 5 iFind the symmetry of the equation7 if any a x 72 y b y 712 iiFind the domain and the solution set of each equation in the real number system 5 7 x 7 3 x 7 4 15 22 1 4 a 7 7 7 b 7 z z 4 z z4 2279 279 23 m L 2z 1 3z i 2 5z 1 Whats the domain ofthe following equation Simplify and nd the solution set of the 3 1 4 equation Check your answer 7 77 x2 7 3x 3 7 z z Solve each inequality Express your answer in interval notation and graph on a number line a 73 172x5 5 b 97le8l 7 c77l2z73l21 Solve each compound inequality Write your solution in interval notation and graph on a number line If there is no solution7 say so a4z524and371lt7 b371lt77and43gt9 Find the center and radius of the circle by completing the square nd also the x7 and y7 intercepts if any x2 y2 7 6x 6y 79 Graph the circle and be sure to mark if there are any intercepts Use the discriminant to determine the type of solution of each equation Use the Quadratic Formula to nd the solution set 2 4 1 2 2 a327171 b42 2 0 c2270 dz36 Find k so that the equation 222 2x 7 k 0 has exactly one real solution p H 0 H H H D H 9 H r H CT 3 0 Solve by factoring a23z278z740 bz4750z2490 d z7lZ3x7113712 0 e x676x39 0 g3 112 23z 112 0 c12 7 5x14 4 6 0 f16z128z11 0 Solve each equation in the real number system Be sure to check your answers a 1272x2z b 2x 7xx11 c x90 lfxa4x7542 nd471 Indicate whether each of the following statements is true or false 1 l 2 b 7 7 7 9 y d If x gt 01 lt 07 then xy 7 z is negative a y4 x4y4 c W 74x 4 H Given the set 76 7x16072 0090833 1227 list all members of the set that are a rational numbers d irrational numbers Rationalize the denominator a b Using distributative rule7 evaluate 356 X 023 7 523 gtlt 092 644 gtlt 023 7 477 gtlt 092 Let a gt 07 if 112 4 fl2 37 nd a2 4 1 2 Find the domain of the expression 475 7 l3x ll 1 b 5sz 7 m Assume z lt 07 evaluate a z 7 3 6 a Determine whether the lines are perpendicular7 paralle or neither L1 5x y 7 3 0 L2 5x 7 y 7 3 0 b Let line one passing through points 271337 and line two passign through points 57 27 717 If two lines are perpendicular to each other7 nd k Use the points 07 797 57 719 on the line7 a nd the slope of the line7 b nd another point on the line

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