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{"name": "2.2.1 Task 2", "extensions": ["jsxgraph"], "custom_part_types": [], "resources": [["question-resources/HELM2_2_Figure7.png", "/srv/numbas/media/question-resources/HELM2_2_Figure7.png"], ["question-resources/HELM2_2_Task1b.png", "/srv/numbas/media/question-resources/HELM2_2_Task1b.png"], ["question-resources/HELM2_2_Figure8.png", "/srv/numbas/media/question-resources/HELM2_2_Figure8.png"], ["question-resources/HELM2_2_Task2.png", "/srv/numbas/media/question-resources/HELM2_2_Task2.png"]], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "2.2.1 Task 2", "tags": [], "metadata": {"description": "<p>Graph the function y=x^2+2 on [-3,3] by plotting points. State the domain and range. This is part of HELM Book 2.2.1.</p>", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "<p>Consider the function given by $f(x)=x^2+2,\\quad -3\\leq x\\leq 3$</p>", "advice": "<p>{xSquaredPlus2}</p>\n<p>This function has domain $[-3,3]$ and range $[2,11]$.</p>", "rulesets": {}, "extensions": ["jsxgraph"], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"xsquaredplus2": {"name": "xsquaredplus2", "group": "Ungrouped variables", "definition": "jessiecode(250, 250, [-4, 12, 4, -1], safe(\"\"\"\n  functiongraph(function(x){return x^2+2;}, -8, 8) <<strokecolor:'black'>>;  \n  point(-3,11) <<color:'black', size:1, withLabel:false>>;\n  point(-2,6) <<color:'black', size:1, withLabel:false>>;\n  point(-1,3) <<color:'black', size:1, withLabel:false>>;\n  point(0,2) <<color:'black', size:1, withLabel:false>>;\n  point(1,3) <<color:'black', size:1, withLabel:false>>;\n  point(2,6) <<color:'black', size:1, withLabel:false>>;\n  point(3,11) <<color:'black', size:1, withLabel:false>>;\n  \"\"\")\n)", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["xsquaredplus2"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": true, "customName": "a)", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>State the domain of the function:</p>\n<p>[[0]] $\\leq x \\leq$ [[1]]</p>\n<p style=\"text-align: center;\"></p>\n<p style=\"text-align: left;\"></p>", "gaps": [{"type": "numberentry", "useCustomName": true, "customName": "x greater than", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "-3", "maxValue": "-3", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": true, "customName": "x less than", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "3", "maxValue": "3", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}, {"type": "gapfill", "useCustomName": true, "customName": "b)", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Draw up a table of input and output values for this function:</p>\n<p>The table of values has been partially calculated. Complete this now:</p>\n<table border=\"s\" style=\"margin-left: auto; margin-right: auto;\">\n<tbody>\n<tr>\n<td style=\"width: 134px;\">input, $x$</td>\n<td style=\"width: 71px;\">-3</td>\n<td style=\"width: 31px;\">-2</td>\n<td style=\"width: 71px;\">-1</td>\n<td style=\"width: 25px;\">0</td>\n<td style=\"width: 65px;\">1</td>\n<td style=\"width: 65px;\">2</td>\n<td style=\"width: 65px;\">3</td>\n</tr>\n<tr>\n<td style=\"width: 134px;\">output,$x^2+2$</td>\n<td style=\"width: 71px;\">[[0]]</td>\n<td style=\"width: 31px;\">6</td>\n<td style=\"width: 71px;\">[[1]]</td>\n<td style=\"width: 25px;\">2</td>\n<td style=\"width: 65px;\">[[2]]</td>\n<td style=\"width: 65px;\">[[3]]</td>\n<td style=\"width: 65px;\">[[4]]</td>\n</tr>\n</tbody>\n</table>\n<p style=\"text-align: center;\"></p>\n<p style=\"text-align: left;\"></p>", "gaps": [{"type": "numberentry", "useCustomName": true, "customName": "x is -3", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "11", "maxValue": "11", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": true, "customName": "x is -1", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "3", "maxValue": "3", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": true, "customName": "x is 1", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "3", "maxValue": "3", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": true, "customName": "x is 2", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "6", "maxValue": "6", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": true, "customName": "x is 3", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "11", "maxValue": "11", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}, {"type": "information", "useCustomName": true, "customName": "c)", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Plot a graph of the function:</p>\n<p>Part of the graph $f(x) = x^2 + 2$ is shown in the figure. Complete it.</p>\n<p style=\"text-align: center;\"><img src=\"resources/question-resources/HELM2_2_Task2.png\"/></p>"}, {"type": "patternmatch", "useCustomName": true, "customName": "d)", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p style=\"text-align: left;\">Deduce the range of the function by inspecting the graph:</p>\n<p style=\"text-align: left;\">(Recall that the range of the function is the set of values that the function takes as x is varied. It is<br/>possible to deduce this from the graph. Write this set as an interval, and don't type any spaces in your answer.)</p>", "answer": "[2,11]", "displayAnswer": "[2,11]", "matchMode": "exact"}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "contributors": [{"name": "Merryn Horrocks", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4052/"}]}]}], "contributors": [{"name": "Merryn Horrocks", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4052/"}]}