// Numbas version: exam_results_page_options
{"name": "Even Functions", "extensions": ["jsxgraph"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"metadata": {"licence": "Creative Commons Attribution-ShareAlike 4.0 International", "description": "<p>A graphical introduction to the concept of even functions a symmery</p>"}, "type": "question", "preamble": {"css": "", "js": ""}, "advice": "<p>Suppose that the point \\(A\\) has coordinates \\((\\var{x1}, \\var{a*x1^2})\\). Then by the symmetry of the graph the point \\(B\\) has coordinates \\((\\var{-1*x1}, \\var{a*x1^2})\\).</p>", "rulesets": {}, "extensions": ["jsxgraph"], "functions": {"graph": {"type": "html", "definition": "var div = Numbas.extensions.jsxgraph.makeBoard('400px','400px',\n{boundingbox: [-2.5, a*6, 2.5, -1],\n axis: true,\n showNavigation: false,\n grid: true\n});\n\nvar board = div.board;\n\nfunction f(x) {\n  return a*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:false, 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 A.Y();}], {name:\"B\",color:\"blue\"});\nvar C = board.createElement('point', [0, function () {return A.Y();}], {name:\"C\",color:\"blue\",visible:false});\n\nboard.createElement('segment', [A,C],{strokeWidth:4});\nboard.createElement('segment', [C,B],{strokeWidth:4,dash:1});\n\nreturn div;", "language": "javascript", "parameters": [["a", "number"]]}}, "ungrouped_variables": ["a", "x1"], "name": "Even Functions", "tags": [], "variablesTest": {"condition": "", "maxRuns": 100}, "variable_groups": [], "variables": {"a": {"name": "a", "definition": "random(1..4)", "group": "Ungrouped variables", "description": "", "templateType": "anything"}, "x1": {"name": "x1", "definition": "random(-2..2 except 0)", "group": "Ungrouped variables", "description": "", "templateType": "anything"}}, "statement": "<p>Geometrically, a function is called <strong>even</strong> if it is symmetric in the <g class=\"gr_ gr_9 gr-alert gr_spell gr_inline_cards gr_run_anim ContextualSpelling ins-del multiReplace\" id=\"9\" data-gr-id=\"9\">veritcal</g> axis. The picture below is an example of an even function because every point \\(A\\) on the curve can be reflected in the vertical axis to produce another point on the curve \\(B\\).</p>\n<p>Here the line from \\(A\\) to the vertical axis is shown as a solid line, and the reflection from the axis to \\(B\\) is shown as a dashed line.</p>\n<p style=\"text-align: center;\">{graph(a)}</p>\n<p style=\"text-align: left;\"><g class=\"gr_ gr_10 gr-alert gr_spell gr_inline_cards gr_run_anim ContextualSpelling ins-del multiReplace\" id=\"10\" data-gr-id=\"10\">Algebraicly</g>, a function has this kind of symmetry whenever</p>\n<p style=\"text-align: center;\">\\(f(-x) \\equiv f(x).\\)</p>", "parts": [{"type": "numberentry", "customMarkingAlgorithm": "", "mustBeReduced": false, "allowFractions": false, "maxValue": "-1*{x1}", "variableReplacementStrategy": "originalfirst", "correctAnswerStyle": "plain", "unitTests": [], "mustBeReducedPC": 0, "notationStyles": ["plain", "en", "si-en"], "prompt": "<p>If the \\(x\\) coordinate of the point \\(A\\) is \\(\\var{x1}\\) then what is the \\(x\\)-coordinate of the point \\(B\\)?</p>", "scripts": {}, "extendBaseMarkingAlgorithm": true, "marks": 1, "minValue": "-1*{x1}", "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "correctAnswerFraction": false}, {"type": "numberentry", "customMarkingAlgorithm": "", "mustBeReduced": false, "allowFractions": false, "maxValue": "{a*x1^2}", "variableReplacementStrategy": "originalfirst", "correctAnswerStyle": "plain", "unitTests": [], "mustBeReducedPC": 0, "notationStyles": ["plain", "en", "si-en"], "prompt": "<p>If the \\(y\\) coordinate of the point \\(A\\) is \\(\\var{a*x1^2}\\) then what is the \\(y\\)-coordinate of the point \\(B\\)?</p>", "scripts": {}, "extendBaseMarkingAlgorithm": true, "marks": 1, "minValue": "{a*x1^2}", "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "correctAnswerFraction": false}], "contributors": [{"name": "Daniel Mansfield", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/743/"}, {"name": "Xiaodan Leng", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2146/"}, {"name": "Laure Helme-Guizon", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2531/"}]}]}], "contributors": [{"name": "Daniel Mansfield", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/743/"}, {"name": "Xiaodan Leng", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2146/"}, {"name": "Laure Helme-Guizon", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2531/"}]}