A graph of $f$ is drawn. Graph of a transformed version of $f$ is to be sketched, by dragging various points around.
", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "The graph of a function $y=f(x)$ is shown below. Move the red points so the red curve represents $y=\\simplify[fractionNumbers,all]{{vsc}f({hsc}x+{hsh})+{vsh}}$.
", "advice": "This involves a mix of transformations. See Lecture ??
", "rulesets": {"std": ["all", "fractionNumbers"]}, "extensions": ["jsxgraph"], "variables": {"hsh": {"name": "hsh", "group": "Ungrouped variables", "definition": "if(selector[1]=1,random(-3..3 except 0),0)", "description": "horizontal shift
", "templateType": "anything"}, "maxy": {"name": "maxy", "group": "Ungrouped variables", "definition": "max(map(abs(a),a,yn)+5)+1", "description": "", "templateType": "anything"}, "yo4": {"name": "yo4", "group": "Ungrouped variables", "definition": "yo[4]", "description": "", "templateType": "anything"}, "vsc": {"name": "vsc", "group": "Ungrouped variables", "definition": "if(selector[2]=1,random(-1,0.5,2),1)", "description": "", "templateType": "anything"}, "recip": {"name": "recip", "group": "Ungrouped variables", "definition": "1/hsc", "description": "", "templateType": "anything"}, "vsh": {"name": "vsh", "group": "Ungrouped variables", "definition": "if(selector[0]=1,random(-3..3#0.5 except 0),0)\n", "description": "vertical shift
", "templateType": "anything"}, "xo": {"name": "xo", "group": "Ungrouped variables", "definition": "list(-2..2)", "description": "original x values
", "templateType": "anything"}, "selector": {"name": "selector", "group": "Ungrouped variables", "definition": "shuffle([1,1,0,0])", "description": "order is ['vsh','hsh','vsc','hsc'] 1 is on 0 is off
", "templateType": "anything"}, "yo1": {"name": "yo1", "group": "Ungrouped variables", "definition": "yo[1]", "description": "", "templateType": "anything"}, "yn": {"name": "yn", "group": "Ungrouped variables", "definition": "map(vsc*y+vsh,y,yo)", "description": "new y values after the transformation
", "templateType": "anything"}, "hsc": {"name": "hsc", "group": "Ungrouped variables", "definition": "if(selector[3]=1,random(-1,1/3,0.5,2),1)", "description": "", "templateType": "anything"}, "yo": {"name": "yo", "group": "Ungrouped variables", "definition": "repeat(random(-5..5),5)", "description": "the (random) original y values which relate to the x values
", "templateType": "anything"}, "yo3": {"name": "yo3", "group": "Ungrouped variables", "definition": "yo[3]", "description": "", "templateType": "anything"}, "xn": {"name": "xn", "group": "Ungrouped variables", "definition": "map((x-hsh)/hsc,x,xo)", "description": "new transformed x values
", "templateType": "anything"}, "maxx": {"name": "maxx", "group": "Ungrouped variables", "definition": "max(map(abs(a),a,xn)+5)+1", "description": "", "templateType": "anything"}, "yo2": {"name": "yo2", "group": "Ungrouped variables", "definition": "yo[2]", "description": "", "templateType": "anything"}, "yo0": {"name": "yo0", "group": "Ungrouped variables", "definition": "yo[0]", "description": "", "templateType": "anything"}}, "variablesTest": {"condition": "(selector[0]+selector[2])=1", "maxRuns": 100}, "ungrouped_variables": ["selector", "vsh", "hsh", "vsc", "hsc", "yo", "yn", "xo", "xn", "yo0", "yo1", "yo2", "yo3", "yo4", "maxx", "maxy", "recip"], "variable_groups": [], "functions": {}, "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;iThe point $A$ was $(-2,\\var{yo0})$ but it is now $\\big($[[0]],[[1]]$\\big)$.
The point $B$ was $(-1,\\var{yo1})$ but it is now $\\big($[[2]],[[3]]$\\big)$.
The point $C$ was $(0,\\var{yo2})$ but it is now $\\big($[[4]],[[5]]$\\big)$.
The point $D$ was $(1,\\var{yo3})$ but it is now $\\big($[[6]],[[7]]$\\big)$.
The point $E$ was $(2,\\var{yo4})$ but it is now $\\big($[[8]],[[9]]$\\big)$.