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1 ## lcao tagged and PAID on 2-20-2004 2 3 ## DBsubject('Algebra') 4 ## DBchapter('Functions') 5 ## DBsection('Transformations of Functions') 6 ## Date('6/3/2002') 7 ## Author('') 8 ## Institution('') 9 ## TitleText1('College Algebra') 10 ## EditionText1('3') 11 ## AuthorText1('Stewart, Redlin, Watson') 12 ## Section1('4.5') 13 ## Problem1('46') 14 DOCUMENT(); # This should be the first executable line in the problem. 15 16 loadMacros( 17 "PG.pl", 18 "PGbasicmacros.pl", 19 "PGchoicemacros.pl", 20 "PGanswermacros.pl", 21 "PGgraphmacros.pl", 22 "PGauxiliaryFunctions.pl" 23 ); 24 25 TEXT(&beginproblem); 26 $showPartialCorrectAnswers = 0; 27 28 $a=random(2,6); 29 $dom = random(2,4); 30 @slice = NchooseK(3,3); 31 $color = "red"; 32 33 $ga = FEQ("${a}*(x*(${dom} - x))*4/(${dom})**2 for x in [0,$dom] using color:red and weight:2"); 34 $gb = FEQ("${a}*(-x * (${dom} + x))*4/(${dom})**2 for x in [-$dom,0] using color:red and weight:2"); 35 36 $graph = init_graph(-8,-8,8,8,'axes'=>[0,0],'grid'=>[16,16]); 37 38 ($gaRef,$gbRef) = plot_functions( $graph,$ga,$gb); 39 40 $graph[0]=init_graph(-8,-8,8,8,'axes'=>[0,0],'grid'=>[16,16]); 41 $graph[1]=init_graph(-8,-8,8,8,'axes'=>[0,0],'grid'=>[16,16]); 42 $graph[2]=init_graph(-8,-8,8,8,'axes'=>[0,0],'grid'=>[16,16]); 43 $graph[3]=init_graph(-8,-8,8,8,'axes'=>[0,0],'grid'=>[16,16]); 44 $graph[4]=init_graph(-8,-8,8,8,'axes'=>[0,0],'grid'=>[16,16]); 45 $graph[5]=init_graph(-8,-8,8,8,'axes'=>[0,0],'grid'=>[16,16]); 46 $graph[6]=init_graph(-8,-8,8,8,'axes'=>[0,0],'grid'=>[16,16]); 47 $graph[7]=init_graph(-8,-8,8,8,'axes'=>[0,0],'grid'=>[16,16]); 48 49 $d2l = $dom - 2; 50 $dn2l =-$dom - 2; 51 $d2r = $dom + 2; 52 $dn2r =-$dom + 2; 53 54 #This is g(x+2)+2 55 $ga1 = FEQ("2+${a}*((x+2)*(${dom}-x-2))*4/(${dom})**2 for x in [-2,$d2l] using color:red and weight:2"); 56 $gb1 = FEQ("2+${a}*(-(x+2)*(${dom}+x+2))*4/(${dom})**2 for x in [$dn2l,-2] using color:red and weight:2"); 57 ($gaRef1,$gbRef1) = plot_functions( $graph[0],$ga1,$gb1); 58 59 #This is g(x+2)-2 60 $ga2 = FEQ("-2+${a}*((x+2)*(${dom}-x-2))*4/(${dom})**2 for x in [-2,$d2l] using color:red and weight:2"); 61 $gb2 = FEQ("-2+${a}*(-(x+2)*(${dom}+x+2))*4/(${dom})**2 for x in [$dn2l,-2] using color:red and weight:2"); 62 ($gaRef2,$gbRef2) = plot_functions( $graph[1],$ga2,$gb2); 63 64 #This is g(x-2)-2 65 $ga3 = FEQ("-2+${a}*((x-2)*(${dom}-x+2))*4/(${dom})**2 for x in [2,$d2r] using color:red and weight:2"); 66 $gb3 = FEQ("-2+${a}*(-(x-2)*(${dom}+x-2))*4/(${dom})**2 for x in [$dn2r,2] using color:red and weight:2"); 67 ($gaRef3,$gbRef3) = plot_functions( $graph[2],$ga3,$gb3); 68 69 #This is g(x-2)+2 70 $ga4 = FEQ("2+${a}*((x-2)*(${dom}-x+2))*4/(${dom})**2 for x in [2,$d2r] using color:red and weight:2"); 71 $gb4 = FEQ("2+${a}*(-(x-2)*(${dom}+x-2))*4/(${dom})**2 for x in [$dn2r,2] using color:red and weight:2"); 72 ($gaRef4,$gbRef4) = plot_functions( $graph[3],$ga4,$gb4); 73 74 $dd2 = $dom / 2; 75 $dnd2 =-$dom / 2; 76 77 #This is g(2x) 78 $ga5 = FEQ("${a}*(2*x*(${dom}-2*x))*4/(${dom})**2 for x in [0,$dd2] using color:red and weight:2"); 79 $gb5 = FEQ("${a}*(-2*x*(${dom}+2*x))*4/(${dom})**2 for x in [$dnd2,0] using color:red and weight:2"); 80 ($gaRef5,$gbRef5) = plot_functions( $graph[4],$ga5,$gb5); 81 82 $dt2 = $dom * 2; 83 $dnt2 =-$dom * 2; 84 85 #This is g(x/2) 86 $ga6 = FEQ("${a}*x*(${dom}-x/2)*4/(2*(${dom})**2) for x in [0,$dt2] using color:red and weight:2"); 87 $gb6 = FEQ("${a}*(-x*(${dom}+x/2))*4/(2*(${dom})**2) for x in [$dnt2,0] using color:red and weight:2"); 88 ($gaRef6,$gbRef6) = plot_functions( $graph[5],$ga6,$gb6); 89 90 #This is 2 + g(-x) 91 $ga7 = FEQ("2+${a}*x*(${dom}-x)*4/($dom)**2 for x in [0,$dom] using color:red and weight:2"); 92 $gb7 = FEQ("2+${a}*(-x*(${dom}+x))*4/($dom)**2 for x in [-$dom,0] using color:red and weight:2"); 93 ($gaRef7,$gbRef7) = plot_functions( $graph[6],$ga7,$gb7); 94 95 #This is 2 - g(x) 96 $ga8 = FEQ("2-${a}*x*(${dom}-x)*4/(${dom})**2 for x in [0,$dom] using color:red and weight:2"); 97 $gb8 = FEQ("2-${a}*(-x*(${dom}+x))*4/(${dom})**2 for x in [-$dom,0] using color:red and weight:2"); 98 ($gaRef8,$gbRef8) = plot_functions( $graph[7],$ga8,$gb8); 99 100 BEGIN_TEXT 101 Let g be the function below.$BR 102 \{ image(insertGraph($graph), width=>200, height=>200) \} 103 $BR 104 The domain of \( g(x) \) is of the form \( [a, b] \), where \( a \) is 105 \{ans_rule(4)\} and \( b \) is \{ans_rule(4)\}. 106 $BR 107 The range of \( g(x) \) is of the form \( [c, d] \), where \( c \) 108 is \{ans_rule(4)\} and \( d \) is \{ans_rule(4)\}. 109 $BR 110 $BR 111 END_TEXT 112 113 ANS(num_cmp(-$dom), num_cmp($dom), num_cmp(0), num_cmp($a)); 114 115 BEGIN_TEXT 116 Enter the letter of the graph which corresponds to each new function defined below: 117 $BR 118 $BR 119 1. \( g(x-2)+2 \) is \{ans_rule(4)\}.$BR 120 2. \( g(2x) \) is \{ans_rule(4)\}.$BR 121 3. \( 2+g(-x) \) is \{ans_rule(4)\}.$BR 122 4. \( g(x+2)-2 \) is \{ans_rule(4)\}.$BR 123 $BR 124 END_TEXT 125 126 @shuffle = NchooseK(8,8); 127 @unshuffle = invert(@shuffle); 128 @answers = 1..8; 129 130 TEXT( 131 begintable(4), 132 row( image( insertGraph($graph[$shuffle[0]]), tex_size => 200), 133 image( insertGraph($graph[$shuffle[1]]), tex_size => 200) , 134 image( insertGraph($graph[$shuffle[2]]), tex_size => 200), 135 image( insertGraph($graph[$shuffle[3]]), tex_size => 200) 136 ), 137 row( 'A','B','C','D'), 138 row( image( insertGraph($graph[$shuffle[4]]), tex_size => 200), 139 image( insertGraph($graph[$shuffle[5]]), tex_size => 200) , 140 image( insertGraph($graph[$shuffle[6]]), tex_size => 200), 141 image( insertGraph($graph[$shuffle[7]]), tex_size => 200) 142 ), 143 row('E','F','G','H'), 144 endtable() 145 ); 146 147 148 &ANS( str_cmp([ @ALPHABET[@unshuffle[3,4,6,1]] ] ) ); 149 150 ENDDOCUMENT(); # This should be the last executable line in the problem.
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