// Numbas version: exam_results_page_options
{"name": "Numbastest uke 35: Funksjoner", "metadata": {"description": "", "licence": "None specified"}, "duration": 0, "percentPass": 0, "showQuestionGroupNames": false, "shuffleQuestionGroups": false, "showstudentname": true, "question_groups": [{"name": "Group", "pickingStrategy": "all-ordered", "pickQuestions": 1, "questionNames": ["", "", "", "", "", "", "", "", "", "", "", "", ""], "variable_overrides": [[], [], [], [], [], [], [], [], [], [], [], [], []], "questions": [{"name": "Beskriver f\u00f8lgende graf en funksjon av x? polynom", "extensions": ["jsxgraph"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Ben Brawn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/605/"}, {"name": "Ida Friestad Pedersen", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/792/"}, {"name": "Elena Malyutina", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7213/"}], "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>Er f&oslash;lgende graf en funksjon av $x$?</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": {}, "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>Grafen beskriver en funksjon av $x$</p>", "<p>Grafen beskriver ikke en funksjon av $x$ $x$</p>"], "matrix": "[funOrNo,abs(1-funOrNo)]"}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "Beskriver f\u00f8lgende graf en funksjon av x?", "extensions": ["jsxgraph"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Ben Brawn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/605/"}, {"name": "Elena Malyutina", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7213/"}], "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>Er f&oslash;lgende graf en funksjon av $x$?</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": {}, "variables": {"no": {"name": "no", "group": "Ungrouped variables", "definition": " random('circle', 'ellipse', 'hhyperbola', 'vhyperbola', 'hbezier', 'vbezier','failstep')", "description": "", "templateType": "anything"}, "funOrNo": {"name": "funOrNo", "group": "Ungrouped variables", "definition": "random(1,0)", "description": "", "templateType": "anything"}, "finalchoice": {"name": "finalchoice", "group": "Ungrouped variables", "definition": "if(funOrNo=1,fun,no)", "description": "", "templateType": "anything"}, "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"}}, "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>en funksjon av $x$</p>", "<p>ikke en funksjon av $x$</p>"], "matrix": "[funOrNo,abs(1-funOrNo)]"}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "Funksjon begrep", "extensions": [], "custom_part_types": [], "resources": [["question-resources/sirkelen.PNG", "/srv/numbas/media/question-resources/sirkelen.PNG"], ["question-resources/parabel.PNG", "/srv/numbas/media/question-resources/parabel.PNG"], ["question-resources/to_mengder_funksjon.PNG", "/srv/numbas/media/question-resources/to_mengder_funksjon.PNG"], ["question-resources/to_mengder_ikke_funksjon.PNG", "/srv/numbas/media/question-resources/to_mengder_ikke_funksjon.PNG"]], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Elena Malyutina", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7213/"}], "tags": [], "metadata": {"description": "", "licence": "None specified"}, "statement": "<p>Hvilke av forholdene under beskriver en funksjon med $x$ som variabel?</p>", "advice": "", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": [], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "m_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, "minMarks": 0, "maxMarks": 0, "shuffleChoices": true, "displayType": "checkbox", "displayColumns": 0, "minAnswers": 0, "maxAnswers": 0, "warningType": "none", "showCellAnswerState": true, "markingMethod": "sum ticked cells", "choices": ["$x$ er lengden av foten i cm\n<div>&nbsp; &nbsp; $y$ er skost&oslash;rrelse&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;</div>", "$x$ er skost&oslash;rrelse<br/>$y$ er lengden av foten i cm", "$x$ er din medstudent<br/>$y$ er et navn p&aring; &eacute;n av hans/hennes s&oslash;sken", "$x$ er din medstudent<br/>$y$ er hans/hennes bursdag", "$x-7y=58$", "$x=y^2-4$", "<img src=\"resources/question-resources/sirkelen.PNG\" width=\"194\" height=\"199\"/>", "<img src=\"resources/question-resources/parabel.PNG\" width=\"197\" height=\"197\"/>", "<table style=\"height: 36px; border-style: none; border-color: #000000;\">\n<tbody>\n<tr style=\"height: 18px;\">\n<td style=\"width: 27px; height: 18px;\">$x$</td>\n<td style=\"width: 25px; height: 18px;\">-7</td>\n<td style=\"width: 18px; height: 18px;\">-2</td>\n<td style=\"width: 16px; height: 18px;\">0</td>\n<td style=\"width: 18px; height: 18px;\">7</td>\n</tr>\n<tr style=\"height: 18px;\">\n<td style=\"width: 27px; height: 18px;\">$y$</td>\n<td style=\"width: 25px; height: 18px;\">-22</td>\n<td style=\"width: 18px; height: 18px;\">15</td>\n<td style=\"width: 16px; height: 18px;\">8</td>\n<td style=\"width: 18px; height: 18px;\">15</td>\n</tr>\n</tbody>\n</table>", "<table style=\"height: 36px;\">\n<tbody>\n<tr style=\"height: 18px;\">\n<td style=\"width: 16px; text-align: center; height: 18px;\">$x$</td>\n<td style=\"width: 16px; text-align: center; height: 18px;\">-2</td>\n<td style=\"width: 16px; text-align: center; height: 18px;\">0</td>\n<td style=\"width: 16px; text-align: center; height: 18px;\">7</td>\n<td style=\"width: 16px; text-align: center; height: 18px;\">7</td>\n</tr>\n<tr style=\"height: 18px;\">\n<td style=\"width: 16px; text-align: center; height: 18px;\">$y$</td>\n<td style=\"width: 16px; text-align: center; height: 18px;\">3</td>\n<td style=\"width: 16px; text-align: center; height: 18px;\">0</td>\n<td style=\"width: 16px; text-align: center; height: 18px;\">-14</td>\n<td style=\"width: 16px; text-align: center; height: 18px;\">11</td>\n</tr>\n</tbody>\n</table>", "<table style=\"height: 36px;\">\n<tbody>\n<tr style=\"height: 18px;\">\n<td style=\"width: 16px; text-align: center; height: 18px;\">$x$</td>\n<td style=\"width: 16px; text-align: center; height: 18px;\">-7</td>\n<td style=\"width: 16px; text-align: center; height: 18px;\">-2</td>\n<td style=\"width: 16px; text-align: center; height: 18px;\">0</td>\n<td style=\"width: 16px; text-align: center; height: 18px;\">7</td>\n</tr>\n<tr style=\"height: 18px;\">\n<td style=\"width: 16px; text-align: center; height: 18px;\">$y$</td>\n<td style=\"width: 16px; text-align: center; height: 18px;\">15</td>\n<td style=\"width: 16px; text-align: center; height: 18px;\">15</td>\n<td style=\"width: 16px; text-align: center; height: 18px;\">15</td>\n<td style=\"width: 16px; text-align: center; height: 18px;\">15</td>\n</tr>\n</tbody>\n</table>", "<img src=\"resources/question-resources/to_mengder_funksjon.PNG\" width=\"210\" height=\"163\"/>", "<img src=\"resources/question-resources/to_mengder_ikke_funksjon.PNG\" width=\"217\" height=\"166\"/>", "$y=\\sqrt{x}$"], "matrix": ["0.5", 0, 0, "0.5", "0.5", 0, 0, "0.5", "0.5", 0, "0.5", "0.5", 0, "0.5"], "distractors": ["", "", "", "", "", "", "", "", "", "", "", "", "", ""]}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "Definisjonsmengden polynom", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Ben Brawn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/605/"}, {"name": "Elena Malyutina", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7213/"}], "tags": [], "metadata": {"description": "<p>Multiple choice <g class=\"gr_ gr_5 gr-alert gr_gramm gr_inline_cards gr_run_anim Grammar multiReplace\" id=\"5\" data-gr-id=\"5\">question</g>. Given a randomised polynomial select the <g class=\"gr_ gr_4 gr-alert gr_spell gr_inline_cards gr_run_anim ContextualSpelling ins-del multiReplace gr-progress sel\" id=\"4\" data-gr-id=\"4\">possibe</g> ways of writing the domain of the function.</p>", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "", "advice": "<p>The function {poly} is a polynomial. Regardless of the value of $\\simplify{{inp}}$, the function $\\simplify{{out}}$ will output a number. That is, the domain of $\\simplify{{out}}$ is the set of all real numbers. We can write this as&nbsp;</p>\n<p>\\[\\text{dom}(\\simplify{{out}})=\\mathbb{R}\\]</p>\n<p>or as the open interval</p>\n<p>\\[\\text{dom}(\\simplify{{out}})=(-\\infty,\\infty).\\]</p>\n<p></p>", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"a": {"name": "a", "group": "Ungrouped variables", "definition": "random(-12..2)", "description": "", "templateType": "anything", "can_override": false}, "c": {"name": "c", "group": "Ungrouped variables", "definition": "[random(-12..12 except 0)]+repeat(random(0,random(-12..12 except 0)),n-1)+[random(-12..12 except 0)]", "description": "", "templateType": "anything", "can_override": false}, "n": {"name": "n", "group": "Ungrouped variables", "definition": "random(1..5)", "description": "", "templateType": "anything", "can_override": false}, "poly": {"name": "poly", "group": "Ungrouped variables", "definition": "if(n=2,'\\$\\\\simplify{{out}({inp})={c[0]}+{c[1]}{inp}+{c[2]}{inp}^2}\\$',\nif(n=3, '\\$\\\\simplify{{out}({inp})={c[0]}+{c[1]}{inp}+{c[2]}{inp}^2+{c[3]}{inp}^3}\\$',\nif(n=4, '\\$\\\\simplify{{out}({inp})={c[0]}+{c[1]}{inp}+{c[2]}{inp}^2+{c[3]}{inp}^3+{c[4]}{inp}^4}\\$',\nif(n=5, '\\$\\\\simplify{{out}({inp})={c[0]}+{c[1]}{inp}+{c[2]}{inp}^2+{c[3]}{inp}^3+{c[4]}{inp}^4+{c[5]}{inp}^5}\\$',\n        '\\$\\\\simplify{{out}({inp})={c[0]}+{c[1]}{inp}}\\$'))))", "description": "", "templateType": "anything", "can_override": false}, "inp": {"name": "inp", "group": "Ungrouped variables", "definition": "expression(random('x','r','s','t','w'))", "description": "", "templateType": "anything", "can_override": false}, "out": {"name": "out", "group": "Ungrouped variables", "definition": "expression(random('f','h','g','p','q','y'))", "description": "", "templateType": "anything", "can_override": false}, "b": {"name": "b", "group": "Ungrouped variables", "definition": "a+random(1..10)", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["out", "inp", "n", "c", "poly", "a", "b"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "m_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>Du f&aring;r oppgitt polynomet {poly} og at dette er definert p&aring; de reelle tallene.</p>\n<p>Hvilke av f&oslash;lgende kan v&aelig;re uttrykk for definisjonsmengden $D_\\simplify{{out}}$ til funksjonen $\\simplify{{out}}(\\simplify{{inp}})$?</p>", "minMarks": 0, "maxMarks": 0, "shuffleChoices": true, "displayType": "checkbox", "displayColumns": "1", "minAnswers": 0, "maxAnswers": 0, "warningType": "none", "showCellAnswerState": true, "markingMethod": "sum ticked cells", "choices": ["<p>$\\mathbb{R}$</p>", "<p>$(-\\infty,\\infty)$</p>", "<p>$\\{\\simplify{{inp}}\\in\\mathbb{R}:\\, \\var{a}\\leq\\simplify{{inp}}\\leq\\var{b}\\}$</p>", "<p>$\\{\\simplify{{inp}}\\in\\mathbb{R}:\\, \\var{a}&lt;\\simplify{{inp}}&lt;\\var{b}\\}$</p>", "<p>$\\{\\simplify{{inp}}\\in\\mathbb{R}:\\, \\simplify{{inp}}\\ne \\var{c[0]}\\}$</p>", "<p>$\\{\\simplify{{inp}}\\in\\mathbb{R}:\\, \\simplify{{inp}}&lt;\\var{a}\\, \\text{or} \\,\\simplify{{inp}}\\ge\\var{b}\\}$</p>"], "matrix": ["0.5", "0.5", 0, 0, 0, 0], "distractors": ["", "", "", "", "", ""]}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "Definisjonsmengden", "extensions": [], "custom_part_types": [], "resources": [["question-resources/parabel_hT6OjoP.PNG", "/srv/numbas/media/question-resources/parabel_hT6OjoP.PNG"], ["question-resources/rot.PNG", "/srv/numbas/media/question-resources/rot.PNG"], ["question-resources/cosinus.PNG", "/srv/numbas/media/question-resources/cosinus.PNG"], ["question-resources/funksjon_tabell.PNG", "/srv/numbas/media/question-resources/funksjon_tabell.PNG"]], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Ida Friestad Pedersen", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/792/"}, {"name": "Elena Malyutina", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7213/"}], "tags": [], "metadata": {"description": "", "licence": "All rights reserved"}, "statement": "<p>For f&oslash;lgende funksjoner $f(x)$ finn definisjonsmengden $D_f$.</p>\n<p>(Figurene er klikkbare)</p>", "advice": "", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": [], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "m_n_x", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minMarks": 0, "maxMarks": 0, "minAnswers": 0, "maxAnswers": 0, "shuffleChoices": false, "shuffleAnswers": true, "displayType": "radiogroup", "warningType": "none", "showCellAnswerState": true, "markingMethod": "sum ticked cells", "choices": ["<img src=\"resources/question-resources/parabel_hT6OjoP.PNG\" width=\"361\" height=\"360\"/>", "<img src=\"resources/question-resources/rot.PNG\" width=\"367\" height=\"275\"/>", "En person jogger hjemmefra til jobb og tilbake. Avstand mellom hjemmet og jobben er 8 km og det tar n&oslash;yaktig to timer. La $x$ v&aelig;re tid og $f(x)$ avstanden hjemmfra.", "<img src=\"resources/question-resources/cosinus.PNG\" width=\"380\" height=\"256\"/>", "<img src=\"resources/question-resources/funksjon_tabell.PNG\" width=\"387\" height=\"77\"/>"], "matrix": [["1", 0, 0, 0, 0, 0, 0, 0], [0, "1", 0, 0, 0, 0, 0, 0], [0, 0, "1", 0, 0, 0, 0, 0], [0, 0, 0, "1", 0, 0, 0, 0], [0, 0, 0, 0, "1", 0, 0, 0]], "layout": {"type": "all", "expression": ""}, "answers": ["$\\mathbb{R}$", "$[0,\\infty)$", "$[0,2]$", "$(0,16]$", "$\\{-7,-2,0,7\\}$", "$[-2,2]$", "$[0,8]$", "$\\{-14,1,3,18\\}$"]}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "Verdismengden", "extensions": [], "custom_part_types": [], "resources": [["question-resources/parabel_hT6OjoP.PNG", "/srv/numbas/media/question-resources/parabel_hT6OjoP.PNG"], ["question-resources/rot.PNG", "/srv/numbas/media/question-resources/rot.PNG"], ["question-resources/cosinus.PNG", "/srv/numbas/media/question-resources/cosinus.PNG"], ["question-resources/funksjon_tabell.PNG", "/srv/numbas/media/question-resources/funksjon_tabell.PNG"]], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Ida Friestad Pedersen", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/792/"}, {"name": "Elena Malyutina", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7213/"}], "tags": [], "metadata": {"description": "", "licence": "All rights reserved"}, "statement": "<p>For f&oslash;lgende $f(x)$ funksjoner finn verdimengden $V_f$.</p>", "advice": "", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": [], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "m_n_x", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minMarks": 0, "maxMarks": 0, "minAnswers": 0, "maxAnswers": 0, "shuffleChoices": false, "shuffleAnswers": true, "displayType": "radiogroup", "warningType": "none", "showCellAnswerState": true, "markingMethod": "sum ticked cells", "choices": ["<img src=\"resources/question-resources/parabel_hT6OjoP.PNG\" width=\"361\" height=\"360\"/>", "<img src=\"resources/question-resources/rot.PNG\" width=\"367\" height=\"275\"/>", "En person jogger hjemmefra til jobb og tilbake. Avstand mellom hjemmet og jobben er 8 km og det tar n&oslash;yaktig to timer. La $x$ v&aelig;re tid og $f(x)$ avstanden hjemmfra.", "<img src=\"resources/question-resources/cosinus.PNG\" width=\"380\" height=\"256\"/>", "<img src=\"resources/question-resources/funksjon_tabell.PNG\" width=\"387\" height=\"77\"/>"], "matrix": [["0", "1", 0, 0, 0, 0, 0, 0], [0, "1", 0, 0, 0, 0, 0, 0], [0, "0", "0", 0, 0, 0, 0, "1"], [0, 0, 0, "1", 0, 0, "1", 0], [0, 0, 0, 0, "1", 0, 0, 0]], "layout": {"type": "all", "expression": ""}, "answers": ["$\\mathbb{R}$", "$[0,\\infty)$", "$[0,2]$", "$(0,16]$", "$[-2,2]$", "$[0,8]$", "$[-14,18]$", "$\\{-14,1,3,18\\}$"]}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "Definisjonsmengden piecewise", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Ben Brawn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/605/"}, {"name": "Elena Malyutina", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7213/"}], "tags": [], "metadata": {"description": "<p>Multiple choice <g class=\"gr_ gr_4 gr-alert gr_gramm gr_inline_cards gr_run_anim Grammar multiReplace\" id=\"4\" data-gr-id=\"4\">question</g>. Given a randomised polynomial select the possible ways of writing the domain of the function.</p>", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "<p>Det er gitt en funksjon</p>", "advice": "<p>The function $\\simplify{{out}}$ is a piecewise function. It is defined on different parts (or pieces) of its domain by different (sub)functions.</p>\n<p></p>\n<p>In particular, the pieces of the domain are the intervals</p>\n<ul>\n<li>$\\simplify{{inp}}&lt; \\var{b0}$</li>\n<li>$\\var{b0}\\leq \\simplify{{inp}}\\leq&nbsp;\\var{b1}$,</li>\n<li>$\\var{b2}\\leq\\simplify{{inp}}&lt; \\var{b3}$,</li>\n<li>$\\var{b3}&lt;\\simplify{{inp}}\\leq \\var{b4}$ and</li>\n<li>$\\simplify{{inp}}\\ge\\var{b5}$.</li>\n</ul>\n<p>and their corresponding (sub)functions are given by the expressions</p>\n<ul>\n<li>$\\simplify{{p0}}$</li>\n<li>$\\simplify{{p1}}$</li>\n<li>$\\simplify{{p2}}$</li>\n<li>$\\simplify{{p3}}$</li>\n<li>$\\simplify{{p4}}$</li>\n</ul>\n<p></p>\n<p>In the case of the function $\\simplify{{out}}$ above, each of the (sub)functions are defined for the indicated intervals and so the domain of $\\simplify{{out}}$ are all of those intervals combined. The first and second interval join nicely without a gap&nbsp;unlike the rest and so we have \\[\\text{dom}(\\simplify{{out}})=\\{\\simplify{{inp}}\\in\\mathbb{R}:\\, \\simplify{{inp}}\\leq \\var{b1},\\; \\var{b2}\\leq \\simplify{{inp}}&lt;\\var{b3},\\; \\var{b3}&lt;\\simplify{{inp}}\\leq\\var{b4}, \\text{ or }\\; \\simplify{{inp}}\\ge \\var{b5}\\}.\\]</p>\n<p></p>", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"b4": {"name": "b4", "group": "Ungrouped variables", "definition": "b[4]", "description": "", "templateType": "anything", "can_override": false}, "p0": {"name": "p0", "group": "Ungrouped variables", "definition": "expression(pieces[0])", "description": "", "templateType": "anything", "can_override": false}, "p4": {"name": "p4", "group": "Ungrouped variables", "definition": "expression(pieces[4])", "description": "", "templateType": "anything", "can_override": false}, "c8": {"name": "c8", "group": "Ungrouped variables", "definition": "random(-12..12 except 0)", "description": "", "templateType": "anything", "can_override": false}, "b": {"name": "b", "group": "Ungrouped variables", "definition": "sort(shuffle(-12..12)[0..6])", "description": "", "templateType": "anything", "can_override": false}, "c7": {"name": "c7", "group": "Ungrouped variables", "definition": "random(-12..12 except 0)", "description": "", "templateType": "anything", "can_override": false}, "out": {"name": "out", "group": "Ungrouped variables", "definition": "expression(random('f','h','g','p','q','y'))", "description": "", "templateType": "anything", "can_override": false}, "p1": {"name": "p1", "group": "Ungrouped variables", "definition": "expression(pieces[1])", "description": "", "templateType": "anything", "can_override": false}, "c1": {"name": "c1", "group": "Ungrouped variables", "definition": "random(-12..12 except 0)", "description": "<p>c</p>", "templateType": "anything", "can_override": false}, "p2": {"name": "p2", "group": "Ungrouped variables", "definition": "expression(pieces[2])", "description": "", "templateType": "anything", "can_override": false}, "b0": {"name": "b0", "group": "Ungrouped variables", "definition": "b[0]", "description": "", "templateType": "anything", "can_override": false}, "c2": {"name": "c2", "group": "Ungrouped variables", "definition": "random(-12..12 except 0)", "description": "", "templateType": "anything", "can_override": false}, "c5": {"name": "c5", "group": "Ungrouped variables", "definition": "random(-12..12 except 0)", "description": "", "templateType": "anything", "can_override": false}, "b5": {"name": "b5", "group": "Ungrouped variables", "definition": "b[5]", "description": "", "templateType": "anything", "can_override": false}, "b3": {"name": "b3", "group": "Ungrouped variables", "definition": "b[3]", "description": "", "templateType": "anything", "can_override": false}, "b1": {"name": "b1", "group": "Ungrouped variables", "definition": "b[1]", "description": "", "templateType": "anything", "can_override": false}, "p3": {"name": "p3", "group": "Ungrouped variables", "definition": "expression(pieces[3])", "description": "", "templateType": "anything", "can_override": false}, "pieces": {"name": "pieces", "group": "Ungrouped variables", "definition": "shuffle(['{c1}{inp}^2+{c2}{inp}+{c3}','{c4}e^{inp}','{c5}{inp}+{c6}','{c7}','{c8}','{inp}','{c5}^{inp}','{c1}{inp}^3','{c8}^({inp}+{c7})', '({inp}+{c6})^2', '({inp}-{c6})^3'])", "description": "", "templateType": "anything", "can_override": false}, "c4": {"name": "c4", "group": "Ungrouped variables", "definition": "random(-12..12 except 0)", "description": "", "templateType": "anything", "can_override": false}, "inp": {"name": "inp", "group": "Ungrouped variables", "definition": "expression(random('x','r','s','t','w'))", "description": "", "templateType": "anything", "can_override": false}, "c3": {"name": "c3", "group": "Ungrouped variables", "definition": "random(-12..12 except 0)", "description": "", "templateType": "anything", "can_override": false}, "b2": {"name": "b2", "group": "Ungrouped variables", "definition": "b[2]", "description": "", "templateType": "anything", "can_override": false}, "c6": {"name": "c6", "group": "Ungrouped variables", "definition": "random(-12..12 except 0)", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["out", "inp", "b", "b0", "b1", "b2", "b3", "b4", "b5", "c1", "c2", "c3", "c4", "c5", "c6", "c7", "c8", "pieces", "p0", "p1", "p2", "p3", "p4"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "m_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>$\\simplify{{out}}(\\simplify{{inp}})=\\left\\{\\begin{align}&amp;\\simplify{{p0}},&amp;&amp; \\text{ for } \\simplify{{inp}}&lt; \\var{b0},&nbsp;\\\\&amp;\\simplify{{p1}},&amp;&amp; \\text{ for } \\var{b0}\\leq \\simplify{{inp}}\\leq&nbsp;\\var{b1},\\\\ &amp;\\simplify{{p2}},&amp;&amp; \\text{ for } \\var{b2}\\leq\\simplify{{inp}}&lt; \\var{b3},\\\\ &amp;\\simplify{{p3}},&amp;&amp; \\text{ for } \\var{b3}&lt;\\simplify{{inp}}\\leq \\var{b4},\\\\ &amp;\\simplify{{p4}},&amp;&amp; \\text{ for } \\simplify{{inp}}\\ge\\var{b5}.\\end{align}\\right.$</p>\n<p></p>\n<p>Hvilke av f&oslash;lgende mengdene er definisjonsmegden til $\\simplify{{out}}(\\simplify{{inp}})$?</p>", "minMarks": 0, "maxMarks": 0, "shuffleChoices": true, "displayType": "checkbox", "displayColumns": "1", "minAnswers": 0, "maxAnswers": 0, "warningType": "none", "showCellAnswerState": true, "markingMethod": "sum ticked cells", "choices": ["<p>$\\text{D}_\\simplify{{out}}=\\mathbb{R}$</p>", "<p>$\\text{D}_\\simplify{{out}}=\\{\\simplify{{inp}}\\in\\mathbb{R}:\\, \\simplify{{inp}}\\leq \\var{b1},\\; \\var{b2}\\leq \\simplify{{inp}}\\leq\\var{b4}, \\text{ or }\\; \\simplify{{inp}}\\ge \\var{b5}\\}$</p>", "<p>$\\text{D}_\\simplify{{out}}=\\{\\simplify{{inp}}\\in\\mathbb{R}:\\, \\simplify{{inp}}\\leq \\var{b1},\\; \\var{b2}\\leq \\simplify{{inp}}&lt;\\var{b3},\\; \\var{b3}&lt;\\simplify{{inp}}\\leq\\var{b4}, \\text{ or }\\; \\simplify{{inp}}\\ge \\var{b5}\\}$</p>", "<p>$\\text{D}_\\simplify{{out}}=\\{\\simplify{{inp}}\\in\\mathbb{R}:\\, \\simplify{{inp}}&lt; \\var{b0},\\; \\var{b2}\\leq \\simplify{{inp}}&lt;\\var{b3},\\; \\var{b3}&lt;\\simplify{{inp}}\\leq\\var{b4}, \\text{ or }\\; \\simplify{{inp}}\\ge \\var{b5}\\}$</p>", "<p>$\\text{D}_\\simplify{{out}}=\\{\\simplify{{inp}}\\in\\mathbb{R}:\\, \\simplify{{inp}}&lt; \\var{b1},\\; \\var{b2}&lt; \\simplify{{inp}}\\leq\\var{b3},\\; \\var{b3}\\leq\\simplify{{inp}}&lt;\\var{b4}, \\text{ or }\\; \\simplify{{inp}}&gt; \\var{b5}\\}$</p>", "<p>$\\text{D}_\\simplify{{out}}=\\mathbb{R}^5$</p>", "<p>$\\text{D}_\\simplify{{out}}=\\{\\simplify{{inp}}\\in\\mathbb{R}:\\, \\simplify{{inp}}&lt; \\var{b0},\\; \\var{b0}&lt; \\simplify{{inp}}&lt;\\var{b1},\\;\\var{b2}\\leq \\simplify{{inp}}&lt;\\var{b3},\\; \\var{b3}&lt;\\simplify{{inp}}\\leq\\var{b4}, \\text{ or }\\; \\simplify{{inp}}\\ge \\var{b5}\\}$</p>"], "matrix": ["0", "0", "1", 0, 0, 0, 0], "distractors": ["", "", "", "", "", "", ""]}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "Kvadratiske funksjoner ax^2+bx+c", "extensions": ["geogebra"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Elena Malyutina", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7213/"}], "tags": [], "metadata": {"description": "", "licence": "All rights reserved"}, "statement": "<p>Finn passende funksjonsuttrykk for hver parabel</p>", "advice": "<p>La $f(x)=ax^2+bx+c$ v&aelig;re en kvadratisk funksjon ($a\\neq0$).&nbsp;</p>\n<p>Hvis $a&gt;0$ har grafen $\\smile$ formen.</p>\n<p>Hvis $a&lt;0$ har grafen $\\frown$ formen.</p>\n<p>$c$ i funskjonsuttrykket blir skj&aelig;ring med $y$ aksen.</p>\n<p>$-\\dfrac{b}{2a}$ er $x$ koordinaten til topp- eller bunnpunkt.</p>", "rulesets": {}, "variables": {"a": {"name": "a", "group": "Ungrouped variables", "definition": "random(-3..3 except 0)", "description": "", "templateType": "anything"}, "b": {"name": "b", "group": "Ungrouped variables", "definition": "random(-10..10 except 0)", "description": "", "templateType": "anything"}, "c": {"name": "c", "group": "Ungrouped variables", "definition": "random(-3..3 except 0)", "description": "", "templateType": "anything"}, "defs1": {"name": "defs1", "group": "Ungrouped variables", "definition": "[\n  ['a',a],\n  ['b',b],\n  ['c',c]\n]", "description": "", "templateType": "anything"}, "defs2": {"name": "defs2", "group": "Ungrouped variables", "definition": "[\n  ['a',-a],\n  ['b',b],\n  ['c',c]\n]", "description": "", "templateType": "anything"}, "defs3": {"name": "defs3", "group": "Ungrouped variables", "definition": "[\n  ['a',1],\n  ['b',-b],\n  ['c',-c]\n]", "description": "", "templateType": "anything"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["a", "b", "c", "defs1", "defs2", "defs3"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "m_n_x", "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>Zoom inn eller ut etter behov</p>", "minMarks": 0, "maxMarks": 0, "minAnswers": 0, "maxAnswers": 0, "shuffleChoices": false, "shuffleAnswers": true, "displayType": "radiogroup", "warningType": "none", "showCellAnswerState": true, "markingMethod": "sum ticked cells", "choices": ["{geogebra_applet('https://www.geogebra.org/m/xr2ykuff',defs1)}", "{geogebra_applet('https://www.geogebra.org/m/xr2ykuff',defs2)}", "{geogebra_applet('https://www.geogebra.org/m/xr2ykuff',defs3)}"], "matrix": [["1", 0, 0], [0, "1", 0], [0, 0, "1"]], "layout": {"type": "all", "expression": ""}, "answers": ["$y=\\simplify{{a}x^2+{b}x+{c}}$", "$y=\\simplify{{-a}x^2+{b}x+{c}}$", "$y=\\simplify{x^2-{b}x-{c}}$"]}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "Kvadratiske funksjoner a(x-k)^2+h", "extensions": ["geogebra"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Elena Malyutina", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7213/"}], "tags": [], "metadata": {"description": "", "licence": "All rights reserved"}, "statement": "<p>Finn passende funksjonsuttrykk for hver parabel</p>", "advice": "<p>La $f(x)=a(x-k)^2+h$ v&aelig;re en kvadratisk funksjon ($a\\neq0$).&nbsp;</p>\n<p>Hvis $a&gt;0$ har grafen $\\smile$ formen.</p>\n<p>Hvis $a&lt;0$ har grafen $\\frown$ formen.</p>\n<p>punktet $(k,h)$ er et top-/bunnpunkt til $f(x)$</p>", "rulesets": {}, "variables": {"a": {"name": "a", "group": "Ungrouped variables", "definition": "random(-3..3 except 0)", "description": "", "templateType": "anything"}, "b": {"name": "b", "group": "Ungrouped variables", "definition": "random(-10..-1)", "description": "", "templateType": "anything"}, "c": {"name": "c", "group": "Ungrouped variables", "definition": "random(0..5)", "description": "", "templateType": "anything"}, "defs1": {"name": "defs1", "group": "Ungrouped variables", "definition": "[\n  ['a',a],\n  ['b',b],\n  ['c',c]\n]", "description": "", "templateType": "anything"}, "defs2": {"name": "defs2", "group": "Ungrouped variables", "definition": "[\n  ['a',-a],\n  ['b',b],\n  ['c',c]\n]", "description": "", "templateType": "anything"}, "defs3": {"name": "defs3", "group": "Ungrouped variables", "definition": "[\n  ['a',1],\n  ['b',c],\n  ['c',b]\n]", "description": "", "templateType": "anything"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["a", "b", "c", "defs1", "defs2", "defs3"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "m_n_x", "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>Zoom inn eller ut etter behov</p>", "minMarks": 0, "maxMarks": 0, "minAnswers": 0, "maxAnswers": 0, "shuffleChoices": false, "shuffleAnswers": true, "displayType": "radiogroup", "warningType": "none", "showCellAnswerState": true, "markingMethod": "sum ticked cells", "choices": ["{geogebra_applet('https://www.geogebra.org/m/fthv9ygu',defs1)}", "{geogebra_applet('https://www.geogebra.org/m/fthv9ygu',defs2)}", "{geogebra_applet('https://www.geogebra.org/m/fthv9ygu',defs3)}"], "matrix": [["1", 0, 0], [0, "1", 0], [0, 0, "1"]], "layout": {"type": "all", "expression": ""}, "answers": ["$y=\\simplify{{a}(x-{b})^2+{c}}$", "$y=\\simplify{{-a}(x-{b})^2+{c}}$", "$y=\\simplify{(x-{c})^2+{b}}$"]}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "Kvadratiske funksjoner a(x-x1)(x-x2)", "extensions": ["geogebra"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Elena Malyutina", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7213/"}], "tags": [], "metadata": {"description": "", "licence": "All rights reserved"}, "statement": "<p>Finn passende funksjonsuttrykk for hver parabel</p>", "advice": "<p>La $f(x)=a(x-x_1)(x-x_2)$ v&aelig;re en kvadratisk funksjon ($a\\neq0$).&nbsp;</p>\n<p>Hvis $a&gt;0$ har grafen $\\smile$ formen.</p>\n<p>Hvis $a&lt;0$ har grafen $\\frown$ formen.</p>\n<p>$x=x_1$, $x=x_2$ er nullpunkter til $f(x)$ eller skj&aelig;ringspunkter med $x$ aksen</p>", "rulesets": {}, "variables": {"a": {"name": "a", "group": "Ungrouped variables", "definition": "random(-3..3 except 0)", "description": "", "templateType": "anything"}, "b": {"name": "b", "group": "Ungrouped variables", "definition": "random(-10..-1)", "description": "", "templateType": "anything"}, "c": {"name": "c", "group": "Ungrouped variables", "definition": "random(0..5)", "description": "", "templateType": "anything"}, "defs1": {"name": "defs1", "group": "Ungrouped variables", "definition": "[\n  ['a',a],\n  ['b',b],\n  ['c',c]\n]", "description": "", "templateType": "anything"}, "defs2": {"name": "defs2", "group": "Ungrouped variables", "definition": "[\n  ['a',-a],\n  ['b',b],\n  ['c',c]\n]", "description": "", "templateType": "anything"}, "defs3": {"name": "defs3", "group": "Ungrouped variables", "definition": "[\n  ['a',1],\n  ['b',b],\n  ['c',b]\n]", "description": "", "templateType": "anything"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["a", "b", "c", "defs1", "defs2", "defs3"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "m_n_x", "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>Zoom inn eller ut etter behov</p>", "minMarks": 0, "maxMarks": 0, "minAnswers": 0, "maxAnswers": 0, "shuffleChoices": false, "shuffleAnswers": true, "displayType": "radiogroup", "warningType": "none", "showCellAnswerState": true, "markingMethod": "sum ticked cells", "choices": ["{geogebra_applet('https://www.geogebra.org/m/qmvgy6dj',defs1)}", "{geogebra_applet('https://www.geogebra.org/m/qmvgy6dj',defs2)}", "{geogebra_applet('https://www.geogebra.org/m/qmvgy6dj',defs3)}"], "matrix": [["1", 0, 0], [0, "1", 0], [0, 0, "1"]], "layout": {"type": "all", "expression": ""}, 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