// Numbas version: exam_results_page_options {"name": "Graphs: Vertical scale transformation", "extensions": ["jsxgraph"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"functions": {}, "ungrouped_variables": ["selector", "vsh", "hsh", "vsc", "hsc", "yo", "yn", "xo", "xn", "yo0", "yo1", "yo2", "yo3", "yo4", "maxx", "maxy"], "name": "Graphs: Vertical scale transformation", "tags": ["functions", "graphing", "graphs", "JSXgraph", "Jsxgraph", "jsxgraph", "transformations"], "advice": "", "rulesets": {"std": ["all", "fractionNumbers"]}, "parts": [{"stepsPenalty": "10", "prompt": "
\n

The 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]]$\\big)$.

$y=\\simplify[fractionNumbers,all]{{vsc}f({hsc}x+{hsh})+{vsh}}$ means that the new graph will be the old graph except the $y$ value of each point on the graph will be $\\var{vsc}$ times what they were before.  half of what they were before. a negative half of what they were before. the negative of what it was before. Since the $y$ value is displayed in the vertical direction, this means the old graph is stretched or scaled vertically by a factor of $\\var{vsc}$ to give the new graph.

", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "scripts": {}, "marks": 0, "showCorrectAnswer": true, "type": "gapfill"}], "statement": "

The graph of a function $y=f(x)$ is shown below. Move the red points so the red curve represents $y=\\simplify[fractionNumbers,all]{{vsc}f({hsc}x+{hsh})+{vsh}}$.

", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "preamble": {"css": "table#values th {\n background: none;\n text-align: center;\n}", "js": "function dragpoint_board() {\n var scope = question.scope;\n \n // var a = scope.variables.a.value;\n// var c = scope.variables.c.value;\n\n var yo0 = scope.variables.yo0.value;\n var yo1 = scope.variables.yo1.value;\n var yo2 = scope.variables.yo2.value;\n var yo3 = scope.variables.yo3.value; \n var yo4 = scope.variables.yo4.value;\n \n var maxx = scope.variables.maxx.value;\n var maxy = scope.variables.maxy.value;\n \n var div = Numbas.extensions.jsxgraph.makeBoard('500px','500px',{boundingBox:[-maxx,maxy,maxx,-maxy],grid:true});\n \$(question.display.html).find('#dragpoint').append(div);\n \n var board = div.board;\n \n \n //create stationary points\n \n var op0 = board.create('point',[-2,yo0],{name:'',fixed:true,size:2,color:'black'});\n var op1 = board.create('point',[-1,yo1],{name:'',fixed:true,size:2,color:'black'});\n var op2 = board.create('point',[0,yo2],{name:'',fixed:true,size:2,color:'black'});\n var op3 = board.create('point',[1,yo3],{name:'',fixed:true,size:2,color:'black'});\n var op4 = board.create('point',[2,yo4],{name:'',fixed:true,size:2,color:'black'});\n \n \n //create draggable points\n //why are there are a cloine under each one?\n var np0 = board.create('point',[-2,yo0],{name:'A',size:2,snapSizeX: 0.25,snapSizeY: 0.25,snapToGrid: true});\n var np1 = board.create('point',[-1,yo1],{name:'B',size:2,snapSizeX: 0.25,snapSizeY: 0.25,snapToGrid: true});\n var np2 = board.create('point',[0,yo2],{name:'C',size:2,snapSizeX: 0.25,snapSizeY: 0.25,snapToGrid: true});\n var np3 = board.create('point',[1,yo3],{name:'D',size:2,snapSizeX: 0.25,snapSizeY: 0.25,snapToGrid: true});\n var np4 = board.create('point',[2,yo4],{name:'E',size:2,snapSizeX: 0.25,snapSizeY: 0.25,snapToGrid: true});\n \n \n \n \n //shorthand to evaluate a mathematical expression to a number\n function evaluate(expression) {\n try {\n var val = Numbas.jme.evaluate(expression,question.scope);\n return Numbas.jme.unwrapValue(val);\n }\n catch(e) {\n // if there's an error, return no number\n return NaN;\n }\n }\n \n // set up points array\n var num_points = 5;\n var points = [np0, np1, np2, np3, np4];\n \n \n // this function sets up the i^th point\n function make_point(i) {\n \n // calculate initial coordinates\n // var x = i-(num_points-1)/2;\n \n // create an invisible vertical line for the point to slide along\n // var line = board.create('line',[[x,0],[x,1]],{visible: false});\n \n // create the point\n // var point = points[i] = board.create(\n // 'point',\n // [i-(num_points-1)/2,0],\n // {\n // name:'',\n // size:2,\n // snapSizeY: 0.25, // the point will snap to y-coordinates which are multiples of 0.1\n // snapSizeX: 0.25,\n // snapToGrid: true\n // }\n // );\n \n var point = points[i];\n \n var x=point[0];\n var y=point[1];\n \n // the contents of the input box for this point\n var xstudentAnswer = question.parts[0].gaps[2*i].display.studentAnswer;\n var ystudentAnswer = question.parts[0].gaps[2*i+1].display.studentAnswer;\n \n // watch the student's input and reposition the point when it changes. \n ko.computed(function() {\n x = evaluate(xstudentAnswer());\n y = evaluate(ystudentAnswer());\n if(!(isNaN(x)) && !(isNaN(y)) && board.mode!=board.BOARD_MODE_DRAG) {\n point.moveTo([x,y],100);\n }\n });\n \n // when the student drags the point, update the gapfill input\n point.on('drag',function(){\n var x = Numbas.math.niceNumber(point.X());\n var y = Numbas.math.niceNumber(point.Y());\n xstudentAnswer(x);\n ystudentAnswer(y);\n });\n \n }\n \n // create each point\n for(var i=0;inew transformed x values

"}, "xo": {"definition": "list(-2..2)", "templateType": "anything", "group": "Ungrouped variables", "name": "xo", "description": "

original x values

"}, "yo": {"definition": "repeat(random(-5..5),5)", "templateType": "anything", "group": "Ungrouped variables", "name": "yo", "description": "

the (random) original y values which relate to the x values

"}, "yn": {"definition": "map(vsc*y+vsh,y,yo)", "templateType": "anything", "group": "Ungrouped variables", "name": "yn", "description": "

new y values after the transformation

"}, "hsh": {"definition": "if(selector='hsh',random(-3..3 except 0),0)", "templateType": "anything", "group": "Ungrouped variables", "name": "hsh", "description": "

horizontal shift

"}, "selector": {"definition": "'vsc'", "templateType": "anything", "group": "Ungrouped variables", "name": "selector", "description": ""}, "vsc": {"definition": "if(selector='vsc',random(-2,-1,-0.5,0.5,2),1)", "templateType": "anything", "group": "Ungrouped variables", "name": "vsc", "description": ""}, "vsh": {"definition": "if(selector='vsh',random(-3..3#0.5 except 0),0)\n", "templateType": "anything", "group": "Ungrouped variables", "name": "vsh", "description": "

vertical shift

"}, "yo4": {"definition": "yo[4]", "templateType": "anything", "group": "Ungrouped variables", "name": "yo4", "description": ""}, "yo3": {"definition": "yo[3]", "templateType": "anything", "group": "Ungrouped variables", "name": "yo3", "description": ""}, "yo2": {"definition": "yo[2]", "templateType": "anything", "group": "Ungrouped variables", "name": "yo2", "description": ""}, "yo1": {"definition": "yo[1]", "templateType": "anything", "group": "Ungrouped variables", "name": "yo1", "description": ""}, "yo0": {"definition": "yo[0]", "templateType": "anything", "group": "Ungrouped variables", "name": "yo0", "description": ""}}, "metadata": {"notes": "", "description": "

of a random cubic spline

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