// Numbas version: exam_results_page_options
{"name": "Maria's copy of Odd Functions", "extensions": ["jsxgraph"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"rulesets": {}, "parts": [{"notationStyles": ["plain", "en", "si-en"], "scripts": {}, "prompt": "<p>If the \\(x\\) coordinate of the point \\(A\\) is \\(\\var{x1}\\) then what is the \\(x\\)-coordinate of the point \\(B\\)?</p>", "maxValue": "-1*{x1}", "unitTests": [], "correctAnswerFraction": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showCorrectAnswer": true, "type": "numberentry", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "customMarkingAlgorithm": "", "customName": "", "showFeedbackIcon": true, "allowFractions": false, "showFractionHint": true, "correctAnswerStyle": "plain", "marks": 1, "extendBaseMarkingAlgorithm": true, "useCustomName": false, "minValue": "-1*{x1}", "adaptiveMarkingPenalty": 0}, {"notationStyles": ["plain", "en", "si-en"], "scripts": {}, "prompt": "<p>If the \\(y\\) coordinate of the point \\(A\\) is \\(\\var{a*x1^3}\\) then what is the \\(y\\)-coordinate of the point \\(B\\)?</p>", "maxValue": "{-a*x1^3}", "unitTests": [], "correctAnswerFraction": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showCorrectAnswer": true, "type": "numberentry", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "customMarkingAlgorithm": "", "customName": "", "showFeedbackIcon": true, "allowFractions": false, "showFractionHint": true, "correctAnswerStyle": "plain", "marks": 1, "extendBaseMarkingAlgorithm": true, "useCustomName": false, "minValue": "{-a*x1^3}", "adaptiveMarkingPenalty": 0}], "name": "Maria's copy of Odd Functions", "variables": {"x1": {"definition": "random(-2..2 except 0)", "description": "", "group": "Ungrouped variables", "templateType": "anything", "name": "x1"}, "a": {"definition": "random(-4..4 except 0)", "description": "", "group": "Ungrouped variables", "templateType": "anything", "name": "a"}}, "functions": {"graph": {"type": "html", "parameters": [["a", "number"]], "language": "javascript", "definition": "var div = Numbas.extensions.jsxgraph.makeBoard('400px','400px',\n{boundingbox: [-2.5, a*8.5, 2.5, -a*8.5],\n axis: true,\n showNavigation: false,\n grid: true\n});\n\nvar board = div.board;\n\nfunction f(x) {\n  return a*x*x*x;\n}\n\nvar curve = board.createElement('functiongraph', f, {visible:true});\n\nvar Y = board.createElement('point', [0,1],{visible:false});\nvar O = board.createElement('point', [0,0],{visible:true, fixed: true, name:\"O\"});\n//var yaxis = board.createElement('line', [Y,O]);\n\nvar A = board.createElement('glider', [-1,a, curve], {name:\"A\"});\nvar B = board.createElement('point', [function () { return -1*A.X();}, function () {return -1*A.Y();}], {name:\"B\",color:\"blue\"});\n//var C = board.createElement('point', [0, function () {return A.Y();}], {name:\"C\",color:\"blue\",visible:false});\n\nboard.createElement('segment', [A,O],{strokeWidth:4});\nboard.createElement('segment', [O,B],{strokeWidth:4,dash:1});\n\nreturn div;"}}, "metadata": {"licence": "Creative Commons Attribution-ShareAlike 4.0 International", "description": "<p>A graphical introduction to the concept of even functions a symmery</p>"}, "statement": "<p>Geometrically, a function is called <strong>odd</strong> if it is symmetric in the origin. The picture below is an example of an odd function because every point \\(A\\) on the curve can be reflected through the origin to produce another point on the curve \\(B\\).</p>\n<p>Here is an example of where the line from \\(A\\) to the vertical axis is shown as a solid line, and the reflection through the origin to \\(B\\) is shown as a dashed line.</p>\n<p style=\"text-align: center;\">{graph(a)}</p>\n<p style=\"text-align: left;\">Algebraicly, a function has this kind of symmetry whenever</p>\n<p style=\"text-align: center;\">\\(f(-x) \\equiv -f(x).\\)</p>", "tags": [], "ungrouped_variables": ["a", "x1"], "variable_groups": [], "preamble": {"css": "", "js": ""}, "advice": "<p>Suppose that the point \\(A\\) has coordinates \\((\\var{x1}, \\var{a*x1^3})\\). Then by the symmetry of the graph the point \\(B\\) has coordinates \\((\\var{-1*x1}, \\var{-a*x1^3})\\).</p>", "extensions": ["jsxgraph"], "variablesTest": {"maxRuns": 100, "condition": ""}, "contributors": [{"name": "Daniel Mansfield", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/743/"}, {"name": "Maria Aneiros", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3388/"}]}]}], "contributors": [{"name": "Daniel Mansfield", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/743/"}, {"name": "Maria Aneiros", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3388/"}]}