// Numbas version: exam_results_page_options
{"name": "Does this graph represent a function of x?", "extensions": ["jsxgraph"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Does this graph represent a function of x?", "tags": [], "metadata": {"description": "<p>A random graph is drawn and students are asked whether it represents a function or not.</p>", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "<p>Does this graph appear to represent a&nbsp;function of $x$?</p>\n<p><span data-jme-visible=\"finalChoice='log' || finalChoice='rechyp' \">Note: A&nbsp;red dashed line represents an asymptote.&nbsp;</span></p>\n<p><span data-jme-visible=\"finalchoice='hstep' || finalchoice='failstep' \">Note: A filled-in circle signifies the point is included in the graph, whereas a hollow circle signifies the point is not included.</span></p>", "advice": "<p>A function is a rule that assigns at most one output (generally a $y$ value) for each input (generally an $x$ value).</p>\n<p></p>\n<p>Graphically, the requirement that there is at most one $y$ value for each $x$ value means a curve is the graph of a function if it passes the 'vertical line test'. That is, if you draw vertical lines through&nbsp;the graph and&nbsp;each vertical line only cuts the graph at most once, the graph 'passes' the vertical line test and it represents a function. In particular the graph shown <span data-jme-visible=\"funOrNo=1\">passes</span> <span data-jme-visible=\"funOrNo=0\">fails</span> the vertical line test and so is <span data-jme-visible=\"funOrNo=0\">not</span> a function.</p>", "rulesets": {}, "extensions": ["jsxgraph"], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"no": {"name": "no", "group": "Ungrouped variables", "definition": " random('circle', 'ellipse', 'hhyperbola', 'vhyperbola', 'hbezier', 'vbezier','failstep')", "description": "", "templateType": "anything", "can_override": false}, "funOrNo": {"name": "funOrNo", "group": "Ungrouped variables", "definition": "random(1,0)", "description": "", "templateType": "anything", "can_override": false}, "finalchoice": {"name": "finalchoice", "group": "Ungrouped variables", "definition": "if(funOrNo=1,fun,no)", "description": "", "templateType": "anything", "can_override": false}, "fun": {"name": "fun", "group": "Ungrouped variables", "definition": "random('constant', 'line', 'sine', 'expi', 'expd','log','quadratic', 'cubic', 'hstep','rechyp')", "description": "<p>http://jsxgraph.uni-bayreuth.de/wiki/index.php/Step_function</p>", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["funOrNo", "fun", "no", "finalchoice"], "variable_groups": [], "functions": {"graph": {"parameters": [["finalchoice", "string"]], "type": "html", "language": "javascript", "definition": "// This function creates the board and sets it up, then returns an\n// HTML div tag containing the board.\n  \n\n\n// First, make the JSXGraph board.\n// The function provided by the JSXGraph extension wraps the board up in \n// a div tag so that it's easier to embed in the page.\nvar div = Numbas.extensions.jsxgraph.makeBoard('400px','400px',\n{boundingBox: [-13,13,13,-13],\n axis: true,\n showNavigation: false,\n grid: true,\n keepaspectratio:true\n});\n  \n// div.board is the object created by JSXGraph, which you use to \n// manipulate elements\nvar board = div.board;  \n\n// create the x-axis.\n//var xaxis = board.create('line',[[0,0],[1,0]], { strokeColor: 'black', fixed: true});\n//var xticks = board.create('ticks',[xaxis,2],{\n//  drawLabels: true,\n//  label: {offset: [-4, -10]},\n//  minorTicks: 0\n//});\n\n// create the y-axis\n//var yaxis = board.create('line',[[0,0],[0,1]], { strokeColor: 'black', fixed: true });\n//var yticks = board.create('ticks',[yaxis,2],{\n//drawLabels: true,\n//label: {offset: [-20, 0]},\n//minorTicks: 0\n//});\n\n//create a random integer function\nfunction getRndInteger(min, max) {\n    return Math.floor(Math.random() * (max - min + 1) ) + min;\n}\n\n\nif (finalchoice=='ellipse'){\nvar f1x=-Math.floor(Math.random() * 5)-1;     \nvar f1y=Math.floor(Math.random() * 10) -5; \nvar f2x=Math.floor(Math.random() * 5)+1;     \nvar f2y=Math.floor(Math.random() * 10) -5; \nvar px=(f1x+f2x)/2+(f2y-f1y)*(0.2+Math.random());     \nvar py=(f1y+f2y)/2+(f1x-f2x)*(0.2+Math.random());\nvar ell = board.create('ellipse',[[f1x,f1y],[f2x,f2y],[px,py]]);\n}\n\n\nif (finalchoice=='circle'){\nvar f1x=getRndInteger(-5,5);     \nvar f1y=getRndInteger(-5,5);    \nvar px=f1x+1+Math.random()*5;     \nvar py=f1y+1+Math.random()*5;\nvar cir = board.create('ellipse',[[f1x,f1y],[f1x,f1y],[px,py]]);\n}\n\n\nif (finalchoice=='hhyperbola'){\nvar f1x=getRndInteger(-7,-2);     \nvar f1y=getRndInteger(-7,7);   \nvar f2x=getRndInteger(0,7);    \nvar bump = Math.random()+1  \nvar f2y=f1y+bump; \nvar px=f2x+1+Math.random();     \nvar py=f2y+1+Math.random();\nvar hhyp = board.create('hyperbola',[[f1x,f1y],[f2x,f2y],[px,py]]);\n}\n\nif (finalchoice=='vhyperbola'){\nvar f1y=getRndInteger(-7,-2);     \nvar f1x=getRndInteger(-7,7);   \nvar f2y=getRndInteger(2,7);    \nvar bump = Math.random()+1  \nvar f2x=f1x+Math.random(); \nvar px=f2x+1+Math.random();     \nvar py=f2y+1+Math.random();\nvar vhyp = board.create('hyperbola',[[f1x,f1y],[f2x,f2y],[px,py]]);\n}\n\n\nif (finalchoice=='hbezier'){\n//some reused values\nvar Ax = getRndInteger(12,15)\nvar Ay = getRndInteger(-10,10)\n  //data points \nvar D1 = board.create('point',[Ax,Ay],{fixed:true,size:-1,name:''});\nvar D2 = board.create('point',[getRndInteger(-15,10), getRndInteger(-15,15)],{fixed:true,size:-1,name:''});  \nvar D3 = board.create('point',[Ax,getRndInteger(-10,10)],{fixed:true,size:-1,name:''});\n  //control points\nvar C1 = board.create('point',[getRndInteger(-15,15), getRndInteger(-15,15)],{fixed:true,size:-1,name:''});\nvar C2 = board.create('point',[getRndInteger(-15,15), getRndInteger(-15,15)],{fixed:true,size:-1,name:''});  \nvar C3 = board.create('point',[getRndInteger(-15,15), getRndInteger(-15,15)],{fixed:true,size:-1,name:''});\nvar C4 = board.create('point',[getRndInteger(-15,15), getRndInteger(-15,15)],{fixed:true,size:-1,name:''});   \n\nvar p = [D1,C1,C2,D2,C3,C4,D3];\nvar hbez = board.create('curve', JXG.Math.Numerics.bezier(p)); \n}\n\nif (finalchoice=='vbezier'){\n//some reused values\nvar Ax = getRndInteger(-5,5)\nvar Ay = getRndInteger(10,15)\n//data points  \nvar D1 = board.create('point',[Ax,Ay],{fixed:true,size:-1,name:''});\nvar D2 = board.create('point',[Ax,-Ay],{fixed:true,size:-1,name:''});  \n//control points \nvar C1 = board.create('point',[getRndInteger(-15,-7), getRndInteger(0,8)],{fixed:true,size:-1,name:''});\nvar C2 = board.create('point',[getRndInteger(7,15), getRndInteger(0,-8)],{fixed:true,size:-1,name:''});  \n  \nvar p = [D1,C1,C2,D2];\nvar vbez = board.create('curve', JXG.Math.Numerics.bezier(p)); \n}\n\nif (finalchoice=='constant'){\n  var b = getRndInteger(-10,10)\n  \nvar con = board.create('functiongraph', [function(x){return b}]);\n}\n\nif (finalchoice=='line'){\n  var b = getRndInteger(-10,10)\n    var m = getRndInteger(-5,5)\n  \nvar lin = board.create('functiongraph', [function(x){return m*x+b}]);\n}\n\nif (finalchoice=='sine'){\n  var a = getRndInteger(1,5)\n  var b = getRndInteger(1,5)\n  var c = getRndInteger(-2,2)\n    var d = getRndInteger(-6,6)\n  \nvar sin = board.create('functiongraph', [function(x){return a*Math.sin(x/b+c)+d}]);\n}\n\nif (finalchoice=='expi'){\n  var a = (-1)**getRndInteger(1,2)*getRndInteger(1,5)\n  var b = Math.random()+1\n  var c = getRndInteger(-2,2)\n    var d = getRndInteger(-6,6)\n  \nvar exp = board.create('functiongraph', [function(x){return a*b**(x+c)+d}]);\n}\n\n\nif (finalchoice=='expd'){\n  var a = (-1)**getRndInteger(1,2)*getRndInteger(1,5)\n  var b = Math.random()+1\n  var c = getRndInteger(-2,2)\n    var d = getRndInteger(-6,6)\n  \nvar exp = board.create('functiongraph', [function(x){return a*b**(-x+c)+d}]);\n}\n\n\nif (finalchoice=='log'){\n  var a = (-1)**getRndInteger(1,2)*getRndInteger(1,5)\n  var b = (-1)**getRndInteger(1,2)*getRndInteger(2,6)\n  var c = getRndInteger(-2,2)\n    var d = getRndInteger(-6,6)\n  \nvar exp = board.create('functiongraph', [function(x){return a*Math.log(x/b+c)+d}]);\n  \nvar p1 = board.create('point',[-c*b,1], {name:'',size:-1});\nvar p2 = board.create('point',[-c*b,-1], {name:'',size:-1});\n  \n  \n  var asy = board.create('line',[p1,p2],{dash:3,strokecolor:'#FF0000'});\n}\n\n\nif (finalchoice=='quadratic'){\n  var r1 = getRndInteger(-8,8)\n  var r2 = getRndInteger(-8,8)\n  var b = getRndInteger(-5,5)\n  var a = (-1)**getRndInteger(1,2)  \n  \nvar quad = board.create('functiongraph', [function(x){return a*(x+r1)*(x+r2)+b}]);\n}\n\nif (finalchoice=='cubic'){\n  var r1 = getRndInteger(-8,8)\n  var r2 = getRndInteger(-8,8)\n  var r3 = getRndInteger(-8,8)\n  var b = getRndInteger(-5,5)\n  var a = (-1)**getRndInteger(1,2)  \n  \nvar cub = board.create('functiongraph', [function(x){return a*(x+r1)*(x+r2)*(x+r3)/10+b}]);\n}\n\n\nif (finalchoice=='hstep'){\n\n var b1 = getRndInteger(-10,-3) ;\n var b2 = getRndInteger(3,10) ;\n var h1 =  getRndInteger(-10,10) ;\n var h2 =  getRndInteger(-10,10) ;\n var h3 =  getRndInteger(-10,10) ;\n\n  \n  var f = function(x) {\n  if(x<b1-0.2)\n    return h1;\n  if(x>=b1 && x <b2-0.2)\n    return h2;\n  if(x>=b2)\n    return h3;\n}\n  \nvar oc1 = board.createElement('circle',[[b1,h1],[b1+0.2,h1+0.2]], {fixed:true,strokewidth:1});\nvar cc1 = board.createElement('circle',[[b1,h2],[b1+0.1,h2+0.1]], {fixed:true,strokewidth:5});\nvar oc2 = board.createElement('circle',[[b2,h2],[b2+0.2,h2+0.2]], {fixed:true,strokewidth:1});\nvar cc2 = board.createElement('circle',[[b2,h3],[b2+0.1,h3+0.1]], {fixed:true,strokewidth:5});\n  \nvar hstep = board.create('functiongraph',[f]);\n}\n\nif (finalchoice=='failstep'){\n\n var b1 = getRndInteger(-10,-3) ;\n var b2 = getRndInteger(3,10) ;\n var h1 =  getRndInteger(-10,10) ;\n var h2 =  getRndInteger(-10,10) ;\n var h3 =  getRndInteger(-10,10) ;\n\n  \n  var f = function(x) {\n  if(x<b1)\n    return h1;\n  if(x>=b1 && x <b2)\n    return h2;\n  if(x>=b2)\n    return h3;\n}\n  \n  var cc1 = board.createElement('circle',[[b1,h1],[b1+0.1,h1+0.1]], {fixed:true,strokewidth:5});\nvar cc2 = board.createElement('circle',[[b1,h2],[b1+0.1,h2+0.1]], {fixed:true,strokewidth:5});\nvar cc3 = board.createElement('circle',[[b2,h2],[b2+0.1,h2+0.1]], {fixed:true,strokewidth:5});\nvar cc4 = board.createElement('circle',[[b2,h3],[b2+0.1,h3+0.1]], {fixed:true,strokewidth:5});\n\n\n  \n  \nvar failstep = board.create('functiongraph',[f]);\n}\n\n\nif (finalchoice=='rechyp'){\n\n var k = (-1)**getRndInteger(1,2)*getRndInteger(1,4) ;\n var x0 = getRndInteger(-7,7) ;\n var y0 =  getRndInteger(-7,7) ;\n\n  \n var f = function(x) {\n return y0+k/(x-x0);\n}\n  \nvar asyh = board.create('line',[[x0,1],[x0,2]],{dash:3,strokecolor:'#FF0000'});\nvar asyv = board.create('line',[[1,y0],[2,y0]],{dash:3,strokecolor:'#FF0000'});\n  \nvar rechyp = board.create('functiongraph',[f]);\n}\n\n\n\nreturn div;"}}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "1_n_2", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>{graph(finalchoice)}</p>", "minMarks": 0, "maxMarks": 0, "shuffleChoices": false, "displayType": "radiogroup", "displayColumns": 0, "showCellAnswerState": true, "choices": ["<p>A function of $x$</p>", "<p>Not a function of $x$</p>"], "matrix": "[funOrNo,abs(1-funOrNo)]"}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "contributors": [{"name": "Ben Brawn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/605/"}]}]}], "contributors": [{"name": "Ben Brawn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/605/"}]}