// Numbas version: exam_results_page_options
{"name": "Sketching Graphs: Vertical translation up", "extensions": ["jsxgraph"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"advice": "<p>This involves a vertical translation.&nbsp;&nbsp;See Lecture 8.4 and Workshop 8.5.</p>", "name": "Sketching Graphs: Vertical translation up", "rulesets": {"std": ["all", "fractionNumbers"]}, "variable_groups": [], "parts": [{"gaps": [{"variableReplacements": [], "maxValue": "xn[0]", "customMarkingAlgorithm": "", "allowFractions": true, "extendBaseMarkingAlgorithm": true, "mustBeReducedPC": 0, "notationStyles": ["plain", "en", "si-en"], "showCorrectAnswer": true, "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "type": "numberentry", "unitTests": [], "marks": "0.2", "showFeedbackIcon": true, "scripts": {}, "mustBeReduced": false, "correctAnswerStyle": "plain", "minValue": "xn[0]"}, {"variableReplacements": [], "maxValue": "yn[0]", "customMarkingAlgorithm": "", "allowFractions": true, "extendBaseMarkingAlgorithm": true, "mustBeReducedPC": 0, "notationStyles": ["plain", "en", "si-en"], "showCorrectAnswer": true, "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "type": "numberentry", "unitTests": [], "marks": "0.2", "showFeedbackIcon": true, "scripts": {}, "mustBeReduced": false, "correctAnswerStyle": "plain", "minValue": "yn[0]"}, {"variableReplacements": [], "maxValue": "xn[1]", "customMarkingAlgorithm": "", "allowFractions": true, "extendBaseMarkingAlgorithm": true, "mustBeReducedPC": 0, "notationStyles": ["plain", "en", "si-en"], "showCorrectAnswer": true, "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "type": "numberentry", "unitTests": [], "marks": "0.2", "showFeedbackIcon": true, "scripts": {}, "mustBeReduced": false, "correctAnswerStyle": "plain", "minValue": "xn[1]"}, {"variableReplacements": [], "maxValue": "yn[1]", "customMarkingAlgorithm": "", "allowFractions": true, "extendBaseMarkingAlgorithm": true, "mustBeReducedPC": 0, "notationStyles": ["plain", "en", "si-en"], "showCorrectAnswer": true, "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "type": "numberentry", "unitTests": [], "marks": "0.2", "showFeedbackIcon": true, "scripts": {}, "mustBeReduced": false, "correctAnswerStyle": "plain", "minValue": "yn[1]"}, {"variableReplacements": [], "maxValue": "xn[2]", "customMarkingAlgorithm": "", "allowFractions": true, "extendBaseMarkingAlgorithm": true, "mustBeReducedPC": 0, "notationStyles": ["plain", "en", "si-en"], "showCorrectAnswer": true, "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "type": "numberentry", "unitTests": [], "marks": "0.2", "showFeedbackIcon": true, "scripts": {}, "mustBeReduced": false, "correctAnswerStyle": "plain", "minValue": "xn[2]"}, {"variableReplacements": [], "maxValue": "yn[2]", "customMarkingAlgorithm": "", "allowFractions": true, "extendBaseMarkingAlgorithm": true, "mustBeReducedPC": 0, "notationStyles": ["plain", "en", "si-en"], "showCorrectAnswer": true, "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "type": "numberentry", "unitTests": [], "marks": "0.2", "showFeedbackIcon": true, "scripts": {}, "mustBeReduced": false, "correctAnswerStyle": "plain", "minValue": "yn[2]"}, {"variableReplacements": [], "maxValue": "xn[3]", "customMarkingAlgorithm": "", "allowFractions": true, "extendBaseMarkingAlgorithm": true, "mustBeReducedPC": 0, "notationStyles": ["plain", "en", "si-en"], "showCorrectAnswer": true, "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "type": "numberentry", "unitTests": [], "marks": "0.2", "showFeedbackIcon": true, "scripts": {}, "mustBeReduced": false, "correctAnswerStyle": "plain", "minValue": "xn[3]"}, {"variableReplacements": [], "maxValue": "yn[3]", "customMarkingAlgorithm": "", "allowFractions": true, "extendBaseMarkingAlgorithm": true, "mustBeReducedPC": 0, "notationStyles": ["plain", "en", "si-en"], "showCorrectAnswer": true, "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "type": "numberentry", "unitTests": [], "marks": "0.2", "showFeedbackIcon": true, "scripts": {}, "mustBeReduced": false, "correctAnswerStyle": "plain", "minValue": "yn[3]"}, {"variableReplacements": [], "maxValue": "xn[4]", "customMarkingAlgorithm": "", "allowFractions": true, "extendBaseMarkingAlgorithm": true, "mustBeReducedPC": 0, "notationStyles": ["plain", "en", "si-en"], "showCorrectAnswer": true, "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "type": "numberentry", "unitTests": [], "marks": "0.2", "showFeedbackIcon": true, "scripts": {}, "mustBeReduced": false, "correctAnswerStyle": "plain", "minValue": "xn[4]"}, {"variableReplacements": [], "maxValue": "yn[4]", "customMarkingAlgorithm": "", "allowFractions": true, "extendBaseMarkingAlgorithm": true, "mustBeReducedPC": 0, "notationStyles": ["plain", "en", "si-en"], "showCorrectAnswer": true, "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "type": "numberentry", "unitTests": [], "marks": "0.2", "showFeedbackIcon": true, "scripts": {}, "mustBeReduced": false, "correctAnswerStyle": "plain", "minValue": "yn[4]"}], "variableReplacements": [], "unitTests": [], "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", "sortAnswers": false, "extendBaseMarkingAlgorithm": true, "customMarkingAlgorithm": "", "showCorrectAnswer": true, "variableReplacementStrategy": "originalfirst", "type": "gapfill", "marks": 0, "showFeedbackIcon": true, "scripts": {}}], "variablesTest": {"maxRuns": 100, "condition": "vsh>0"}, "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>", "preamble": {"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}); ", "css": "table#values th {\n  background: none;\n  text-align: center;\n}"}, "metadata": {"description": "<p>A graph of $f$ is drawn. Graph of a transformed version of $f$ is to be sketched, by dragging various points around.</p>", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "variables": {"yo0": {"name": "yo0", "definition": "yo[0]", "group": "Ungrouped variables", "description": "", "templateType": "anything"}, "xo": {"name": "xo", "definition": "list(-2..2)", "group": "Ungrouped variables", "description": "<p>original x values</p>", "templateType": "anything"}, "selector": {"name": "selector", "definition": "[1,0,0,0]", "group": "Ungrouped variables", "description": "<p>order is ['vsh','hsh','vsc','hsc'] 1 is on 0 is off</p>", "templateType": "anything"}, "yo4": {"name": "yo4", "definition": "yo[4]", "group": "Ungrouped variables", "description": "", "templateType": "anything"}, "maxy": {"name": "maxy", "definition": "max(map(abs(a),a,yn)+5)+1", "group": "Ungrouped variables", "description": "", "templateType": "anything"}, "hsc": {"name": "hsc", "definition": "if(selector[3]=1,random(-2,-1,-0.5,0.5,2),1)", "group": "Ungrouped variables", "description": "", "templateType": "anything"}, "maxx": {"name": "maxx", "definition": "max(map(abs(a),a,xn)+5)+1", "group": "Ungrouped variables", "description": "", "templateType": "anything"}, "yo2": {"name": "yo2", "definition": "yo[2]", "group": "Ungrouped variables", "description": "", "templateType": "anything"}, "vsh": {"name": "vsh", "definition": "if(selector[0]=1,random(-3..3#0.5 except 0),0)\n", "group": "Ungrouped variables", "description": "<p>vertical shift</p>", "templateType": "anything"}, "xn": {"name": "xn", "definition": "map((x-hsh)/hsc,x,xo)", "group": "Ungrouped variables", "description": "<p>new transformed x values</p>", "templateType": "anything"}, "vsc": {"name": "vsc", "definition": "if(selector[2]=1,random(-2,-1,-0.5,0.5,2),1)", "group": "Ungrouped variables", "description": "", "templateType": "anything"}, "yn": {"name": "yn", "definition": "map(vsc*y+vsh,y,yo)", "group": "Ungrouped variables", "description": "<p>new y values after the transformation</p>", "templateType": "anything"}, "yo3": {"name": "yo3", "definition": "yo[3]", "group": "Ungrouped variables", "description": "", "templateType": "anything"}, "yo1": {"name": "yo1", "definition": "yo[1]", "group": "Ungrouped variables", "description": "", "templateType": "anything"}, "hsh": {"name": "hsh", "definition": "if(selector[1]=1,random(-3..3 except 0),0)", "group": "Ungrouped variables", "description": "<p>horizontal shift</p>", "templateType": "anything"}, "recip": {"name": "recip", "definition": "1/hsc", "group": "Ungrouped variables", "description": "", "templateType": "anything"}, "yo": {"name": "yo", "definition": "repeat(random(-5..5),5)", "group": "Ungrouped variables", "description": "<p>the (random) original y values which relate to the x values</p>", "templateType": "anything"}}, "functions": {}, "tags": [], "ungrouped_variables": ["selector", "vsh", "hsh", "vsc", "hsc", "yo", "yn", "xo", "xn", "yo0", "yo1", "yo2", "yo3", "yo4", "maxx", "maxy", "recip"], "extensions": ["jsxgraph"], "type": "question", "contributors": [{"name": "Lovkush Agarwal", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1358/"}]}]}], "contributors": [{"name": "Lovkush Agarwal", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1358/"}]}