// Numbas version: finer_feedback_settings
{"name": "Graphs: Random Single Transformation", "extensions": ["jsxgraph"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"advice": "", "parts": [{"stepsPenalty": "10", "steps": [{"prompt": "<p><span data-jme-visible=\"hsc&lt;&gt;1\">$y=\\simplify[fractionNumbers,all]{{vsc}f({hsc}x+{hsh})+{vsh}}$ means that to get the same $y$ value as the original graph the new $x$ value will have to be <span data-jme-visible=\"hsc=0.5\">$2$ times</span> <span data-jme-visible=\"hsc=-0.5\">$-2$ times</span> <span data-jme-visible=\"hsc=-1\">the negative of</span> <span data-jme-visible=\"hsc=2\">half of</span> <span data-jme-visible=\"hsc=-2\">the negative half of</span> what it was&nbsp;before&nbsp;(so that when you&nbsp;multiply the&nbsp;new $x$ value by $\\var{hsc}$ you get the old one).</span></p>\n<p><span data-jme-visible=\"hsc&lt;&gt;1\">Since the $x$ value is displayed in the horizontal&nbsp;direction, this means&nbsp;the old graph is&nbsp;stretched&nbsp;or&nbsp;scaled horizontally&nbsp;by a factor of $\\simplify[fractionNumbers,all]{{recip}}$ to give the new graph<span data-jme-visible=\"hsc&lt;&gt;-1\">, or in other words, compressed horizontally by a factor of $\\simplify[fractionNumbers,all]{{hsc}}$</span>.</span></p>\n<p><span data-jme-visible=\"hsh&lt;&gt;0\">$y=\\simplify[fractionNumbers,all]{{vsc}f({hsc}x+{hsh})+{vsh}}$ means that to get the same $y$ value as the original graph the new $x$ value will have to be $\\var{abs(hsh)}$ unit<span data-jme-visible=\"abs(hsh)&gt;1\">s</span>&nbsp;<span data-jme-visible=\"hsh&gt;0\">less</span> <span data-jme-visible=\"hsh&lt;0\">greater</span> than the original $x$ value (so that when you <span data-jme-visible=\"hsh&gt;0\">add $\\var{hsh}$ to</span>&nbsp;<span data-jme-visible=\"hsh&lt;0\">subtract $\\var{abs(hsh)}$ from</span>&nbsp;the new $x$ value you get the old one).</span></p>\n<p><span data-jme-visible=\"hsh&lt;&gt;0\">Since the $x$ value is displayed in the horizontal&nbsp;direction, this means&nbsp;the old graph is shifted horizontally&nbsp;$\\var{abs(hsh)}$ unit<span data-jme-visible=\"abs(hsh)&gt;1\">s</span> to the&nbsp;<span data-jme-visible=\"hsh&gt;0\">left</span> <span data-jme-visible=\"hsh&lt;0\">right</span> to give the new graph.</span></p>\n<p><span data-jme-visible=\"vsh&lt;&gt;0\">$y=\\simplify[fractionNumbers,all]{{vsc}f({hsc}x+{hsh})+{vsh}}$ means that the new graph will be the old graph except the $y$ value of each point on the graph will be $\\var{abs(vsh)}$ unit<span data-jme-visible=\"abs(vsh)&lt;&gt;1\">s</span>&nbsp;<span data-jme-visible=\"vsh&gt;0\">greater</span> <span data-jme-visible=\"vsh&lt;0\">less</span> than they were before. Since the $y$ value is displayed in the vertical direction, this means&nbsp;the old graph is shifted vertically by $\\var{vsh}$ unit<span data-jme-visible=\"abs(vsh)&lt;&gt;1\">s</span> to give the new graph.</span></p>\n<p><span data-jme-visible=\"vsc&lt;&gt;1\">$y=\\simplify[fractionNumbers,all]{{vsc}f({hsc}x+{hsh})+{vsh}}$ means that the new graph will be the old graph except the $y$ value of each point on the graph will be <span data-jme-visible=\"abs(vsc)=2\">$\\var{vsc}$ times what they were before.</span>&nbsp; <span data-jme-visible=\"vsc=0.5\">half of what they were before.</span><span data-jme-visible=\"vsc=-0.5\">&nbsp;a negative half of what they were before.</span>&nbsp;<span data-jme-visible=\"vsc=-1\">the negative of what it was before.</span> Since the $y$ value is displayed in the vertical direction, this means&nbsp;the old graph is stretched&nbsp;or&nbsp;scaled&nbsp;vertically by a factor of $\\var{vsc}$ to give the new graph.&nbsp;</span></p>", "marks": 0, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "scripts": {}, "showCorrectAnswer": true, "type": "information"}], "marks": 0, "prompt": "<div id=\"dragpoint\"></div>\n<p>The point $A$ was $(-2,\\var{yo0})$ but it is now $\\big($[[0]],[[1]]$\\big)$.<br/>The point $B$ was $(-1,\\var{yo1})$ but it is now $\\big($[[2]],[[3]]$\\big)$.<br/>The point $C$ was $(0,\\var{yo2})$ but it is now $\\big($[[4]],[[5]]$\\big)$.<br/>The point $D$ was $(1,\\var{yo3})$ but it is now $\\big($[[6]],[[7]]$\\big)$.<br/>The point $E$ was $(2,\\var{yo4})$ but it is now $\\big($[[8]],[[9]]$\\big)$.</p>\n", "gaps": [{"maxValue": "xn[0]", "allowFractions": true, "correctAnswerFraction": false, "marks": 1, "minValue": "xn[0]", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "scripts": {}, "showCorrectAnswer": true, "showPrecisionHint": false, "type": "numberentry"}, {"maxValue": "yn[0]", "allowFractions": true, "correctAnswerFraction": false, "marks": 1, "minValue": "yn[0]", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "scripts": {}, "showCorrectAnswer": true, "showPrecisionHint": false, "type": "numberentry"}, {"maxValue": "xn[1]", "allowFractions": true, "correctAnswerFraction": false, "marks": 1, "minValue": "xn[1]", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "scripts": {}, "showCorrectAnswer": true, "showPrecisionHint": false, "type": "numberentry"}, {"maxValue": "yn[1]", "allowFractions": true, "correctAnswerFraction": false, "marks": 1, "minValue": "yn[1]", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "scripts": {}, "showCorrectAnswer": true, "showPrecisionHint": false, "type": "numberentry"}, {"maxValue": "xn[2]", "allowFractions": true, "correctAnswerFraction": false, "marks": 1, "minValue": "xn[2]", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "scripts": {}, "showCorrectAnswer": true, "showPrecisionHint": false, "type": "numberentry"}, {"maxValue": "yn[2]", "allowFractions": true, "correctAnswerFraction": false, "marks": 1, "minValue": "yn[2]", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "scripts": {}, "showCorrectAnswer": true, "showPrecisionHint": false, "type": "numberentry"}, {"maxValue": "xn[3]", "allowFractions": true, "correctAnswerFraction": false, "marks": 1, "minValue": "xn[3]", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "scripts": {}, "showCorrectAnswer": true, "showPrecisionHint": false, "type": "numberentry"}, {"maxValue": "yn[3]", "allowFractions": true, "correctAnswerFraction": false, "marks": 1, "minValue": "yn[3]", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "scripts": {}, "showCorrectAnswer": true, "showPrecisionHint": false, "type": "numberentry"}, {"maxValue": "xn[4]", "allowFractions": true, "correctAnswerFraction": false, "marks": 1, "minValue": "xn[4]", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "scripts": {}, "showCorrectAnswer": true, "showPrecisionHint": false, "type": "numberentry"}, {"maxValue": "yn[4]", "allowFractions": true, "correctAnswerFraction": false, "marks": 1, "minValue": "yn[4]", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "scripts": {}, "showCorrectAnswer": true, "showPrecisionHint": false, "type": "numberentry"}], "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "scripts": {}, "showCorrectAnswer": true, "type": "gapfill"}], "variable_groups": [], "ungrouped_variables": ["selector", "vsh", "hsh", "vsc", "hsc", "yo", "yn", "xo", "xn", "yo0", "yo1", "yo2", "yo3", "yo4", "maxx", "maxy", "recip"], "rulesets": {"std": ["all", "fractionNumbers"]}, "name": "Graphs: Random Single Transformation", "tags": ["functions", "graphing", "graphs", "JSXgraph", "Jsxgraph", "jsxgraph", "transformations"], "type": "question", "functions": {}, "preamble": {"css": "table#values th {\n  background: none;\n  text-align: center;\n}", "js": "function dragpoint_board() {\n  var scope = question.scope;\n  \n // var a = scope.variables.a.value;\n//  var c = scope.variables.c.value;\n\n  var yo0 = scope.variables.yo0.value;\n  var yo1 = scope.variables.yo1.value;\n  var yo2 = scope.variables.yo2.value;\n  var yo3 = scope.variables.yo3.value;  \n  var yo4 = scope.variables.yo4.value;\n    \n  var maxx = scope.variables.maxx.value;\n  var maxy = scope.variables.maxy.value;\n  \n  var div = Numbas.extensions.jsxgraph.makeBoard('500px','500px',{boundingBox:[-maxx,maxy,maxx,-maxy],grid:true});\n  $(question.display.html).find('#dragpoint').append(div);\n  \n  var board = div.board;\n  \n  \n   //create stationary points\n    \n  var op0 = board.create('point',[-2,yo0],{name:'',fixed:true,size:2,color:'black'});\n    var op1 = board.create('point',[-1,yo1],{name:'',fixed:true,size:2,color:'black'});\n    var op2 = board.create('point',[0,yo2],{name:'',fixed:true,size:2,color:'black'});\n    var op3 = board.create('point',[1,yo3],{name:'',fixed:true,size:2,color:'black'});\n    var op4 = board.create('point',[2,yo4],{name:'',fixed:true,size:2,color:'black'});\n    \n    \n    //create draggable points\n    //why are there are a cloine under each one?\n    var np0 = board.create('point',[-2,yo0],{name:'A',size:2,snapSizeX: 0.25,snapSizeY: 0.25,snapToGrid: true});\n    var np1 = board.create('point',[-1,yo1],{name:'B',size:2,snapSizeX: 0.25,snapSizeY: 0.25,snapToGrid: true});\n    var np2 = board.create('point',[0,yo2],{name:'C',size:2,snapSizeX: 0.25,snapSizeY: 0.25,snapToGrid: true});\n    var np3 = board.create('point',[1,yo3],{name:'D',size:2,snapSizeX: 0.25,snapSizeY: 0.25,snapToGrid: true});\n    var np4 = board.create('point',[2,yo4],{name:'E',size:2,snapSizeX: 0.25,snapSizeY: 0.25,snapToGrid: true});\n  \n  \n    \n  \n  //shorthand to evaluate a mathematical expression to a number\n  function evaluate(expression) {\n    try {\n      var val = Numbas.jme.evaluate(expression,question.scope);\n      return Numbas.jme.unwrapValue(val);\n    }\n    catch(e) {\n      // if there's an error, return no number\n      return NaN;\n    }\n  }\n  \n  // set up points array\n  var num_points = 5;\n  var points = [np0, np1, np2, np3, np4];\n  \n  \n  // this function sets up the i^th point\n  function make_point(i) {\n    \n    // calculate initial coordinates\n  //  var x = i-(num_points-1)/2;\n    \n    // create an invisible vertical line for the point to slide along\n   // var line = board.create('line',[[x,0],[x,1]],{visible: false});\n    \n    // create the point\n  //  var point = points[i] = board.create(\n   //   'point',\n   //   [i-(num_points-1)/2,0],\n   //   {\n    //    name:'',\n   //     size:2,\n    //    snapSizeY: 0.25,  // the point will snap to y-coordinates which are multiples of 0.1\n    //    snapSizeX: 0.25,\n   //     snapToGrid: true\n    //  }\n   // );\n    \n   var point = points[i];\n    \n    var x=point[0];\n    var y=point[1];\n    \n    // the contents of the input box for this point\n    var xstudentAnswer = question.parts[0].gaps[2*i].display.studentAnswer;\n    var ystudentAnswer = question.parts[0].gaps[2*i+1].display.studentAnswer;\n    \n    // watch the student's input and reposition the point when it changes.    \n    ko.computed(function() {\n      x = evaluate(xstudentAnswer());\n      y = evaluate(ystudentAnswer());\n      if(!(isNaN(x)) && !(isNaN(y)) && board.mode!=board.BOARD_MODE_DRAG) {\n        point.moveTo([x,y],100);\n      }\n    });\n    \n    // when the student drags the point, update the gapfill input\n    point.on('drag',function(){\n      var x = Numbas.math.niceNumber(point.X());\n      var y = Numbas.math.niceNumber(point.Y());\n      xstudentAnswer(x);\n      ystudentAnswer(y);\n    });\n    \n  }\n  \n  // create each point\n  for(var i=0;i<num_points;i++) {\n    make_point(i);\n  }\n  \n  // create the parabola\n  var parabool = board.create('spline',[np0, np1, np2, np3, np4],{strokeWidth:3,strokeColor:'red'});\n  var statparabool = board.create('spline',[op0, op1, op2, op3, op4],{strokeWidth:3,strokeColor:'black'});\n\n}\n\nquestion.signals.on('HTMLAttached',function() {\n  dragpoint_board();\n}); "}, "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "questions": [], "pickQuestions": 0}], "variablesTest": {"condition": "", "maxRuns": 100}, "metadata": {"description": "<p>Horizontal and vertical shifts and scales of a random cubic spline</p>", "notes": "", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "<p>The&nbsp;graph of a function $y=f(x)$ is shown below. Move the red points so the red curve represents $y=\\simplify[fractionNumbers,all]{{vsc}f({hsc}x+{hsh})+{vsh}}$.</p>", "variables": {"maxx": {"templateType": "anything", "definition": "max(map(abs(a),a,xn)+5)+1", "description": "", "group": "Ungrouped variables", "name": "maxx"}, "maxy": {"templateType": "anything", "definition": "max(map(abs(a),a,yn)+5)+1", "description": "", "group": "Ungrouped variables", "name": "maxy"}, "yo4": {"templateType": "anything", "definition": "yo[4]", "description": "", "group": "Ungrouped variables", "name": "yo4"}, "yo3": {"templateType": "anything", "definition": "yo[3]", "description": "", "group": "Ungrouped variables", "name": "yo3"}, "vsh": {"templateType": "anything", "definition": "if(selector='vsh',random(-3..3#0.5 except 0),0)\n", "description": "<p>vertical shift</p>", "group": "Ungrouped variables", "name": "vsh"}, "yo2": {"templateType": "anything", "definition": "yo[2]", "description": "", "group": "Ungrouped variables", "name": "yo2"}, "yo": {"templateType": "anything", "definition": "repeat(random(-5..5),5)", "description": "<p>the (random) original y values which relate to the x values</p>", "group": "Ungrouped variables", "name": "yo"}, "yo1": {"templateType": "anything", "definition": "yo[1]", "description": "", "group": "Ungrouped variables", "name": "yo1"}, "yn": {"templateType": "anything", "definition": "map(vsc*y+vsh,y,yo)", "description": "<p>new y values after the transformation</p>", "group": "Ungrouped variables", "name": "yn"}, "hsc": {"templateType": "anything", "definition": "if(selector='hsc',random(-2,-1,-0.5,0.5,2),1)", "description": "", "group": "Ungrouped variables", "name": "hsc"}, "xo": {"templateType": "anything", "definition": "list(-2..2)", "description": "<p>original x values</p>", "group": "Ungrouped variables", "name": "xo"}, "recip": {"templateType": "anything", "definition": "1/hsc", "description": "", "group": "Ungrouped variables", "name": "recip"}, "hsh": {"templateType": "anything", "definition": "if(selector='hsh',random(-3..3 except 0),0)", "description": "<p>horizontal shift</p>", "group": "Ungrouped variables", "name": "hsh"}, "selector": {"templateType": "anything", "definition": "random('vsh','hsh','vsc','hsc')", "description": "", "group": "Ungrouped variables", "name": "selector"}, "yo0": {"templateType": "anything", "definition": "yo[0]", "description": "", "group": "Ungrouped variables", "name": "yo0"}, "vsc": {"templateType": "anything", "definition": "if(selector='vsc',random(-2,-1,-0.5,0.5,2),1)", "description": "", "group": "Ungrouped variables", "name": "vsc"}, "xn": {"templateType": "anything", "definition": "map((x-hsh)/hsc,x,xo)", "description": "<p>new transformed x values</p>", "group": "Ungrouped variables", "name": "xn"}}, "contributors": [{"name": "Ben Brawn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/605/"}, {"name": "Xiaodan Leng", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2146/"}]}]}], "contributors": [{"name": "Ben Brawn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/605/"}, {"name": "Xiaodan Leng", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2146/"}]}