// Numbas version: exam_results_page_options
{"name": "PreCal Function Analysis", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"rulesets": {}, "preamble": {"js": "", "css": ""}, "variablesTest": {"condition": "", "maxRuns": 100}, "variable_groups": [], "tags": [], "ungrouped_variables": ["A", "B", "C", "cx2", "cx", "cc", "aq", "bq", "cq", "lc", "cx3", "reLeft", "reRight", "max", "min", "xval", "fofXval"], "functions": {}, "name": "PreCal Function Analysis", "advice": "", "metadata": {"licence": "All rights reserved", "description": ""}, "extensions": [], "variables": {"reLeft": {"definition": "precround((-bq-sqrt(bq*bq-4*aq*cq))/(2*aq),3)", "templateType": "anything", "group": "Ungrouped variables", "name": "reLeft", "description": ""}, "max": {"definition": "vector(reLeft,precround((reLeft+A)*(reLeft+B)*(reLeft+C),3))", "templateType": "anything", "group": "Ungrouped variables", "name": "max", "description": ""}, "cx2": {"definition": "lc*(A+B+C)", "templateType": "anything", "group": "Ungrouped variables", "name": "cx2", "description": ""}, "cq": {"definition": "cx", "templateType": "anything", "group": "Ungrouped variables", "name": "cq", "description": ""}, "cx": {"definition": "lc*(A*B+A*C+B*C)", "templateType": "anything", "group": "Ungrouped variables", "name": "cx", "description": ""}, "reRight": {"definition": "precround((-bq+sqrt(bq*bq-4*aq*cq))/(2*aq),3)", "templateType": "anything", "group": "Ungrouped variables", "name": "reRight", "description": ""}, "lc": {"definition": "1", "templateType": "anything", "group": "Ungrouped variables", "name": "lc", "description": ""}, "bq": {"definition": "2*cx2", "templateType": "anything", "group": "Ungrouped variables", "name": "bq", "description": ""}, "B": {"definition": "random(-2..2#0.25 except A)", "templateType": "anything", "group": "Ungrouped variables", "name": "B", "description": ""}, "aq": {"definition": "3", "templateType": "anything", "group": "Ungrouped variables", "name": "aq", "description": ""}, "xval": {"definition": "random(-3..-1#0.1)", "templateType": "anything", "group": "Ungrouped variables", "name": "xval", "description": ""}, "cc": {"definition": "lc*(A*B*C)", "templateType": "anything", "group": "Ungrouped variables", "name": "cc", "description": ""}, "fofXval": {"definition": "precround((xval+A)*(xval+B)*(xval+C),3)", "templateType": "anything", "group": "Ungrouped variables", "name": "fofXval", "description": ""}, "C": {"definition": "random(3..5#0.25 except [A,B])\n", "templateType": "anything", "group": "Ungrouped variables", "name": "C", "description": ""}, "cx3": {"definition": "lc", "templateType": "anything", "group": "Ungrouped variables", "name": "cx3", "description": ""}, "A": {"definition": "random(-5..-3#0.25)", "templateType": "anything", "group": "Ungrouped variables", "name": "A", "description": ""}, "min": {"definition": "vector(reRight,precround((reRight+A)*(reRight+B)*(reRight+C),3))", "templateType": "anything", "group": "Ungrouped variables", "name": "min", "description": ""}}, "parts": [{"showFeedbackIcon": true, "type": "jme", "prompt": "<p>What are the x-intercepts of $f(x)$?&nbsp;&nbsp;</p>\n<p><em>In your response use the format:&nbsp;&nbsp;<strong>set(-2,3,5)&nbsp;</strong>for example</em></p>", "showPreview": true, "variableReplacements": [], "vsetRangePoints": 5, "failureRate": 1, "customName": "", "answer": "set(-{A},-{B},-{C})", "showCorrectAnswer": true, "unitTests": [], "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "vsetRange": [0, 1], "variableReplacementStrategy": "originalfirst", "valuegenerators": [], "useCustomName": false, "checkingType": "absdiff", "adaptiveMarkingPenalty": 0, "checkingAccuracy": 0.001, "marks": 1, "scripts": {}, "checkVariableNames": false}, {"showFeedbackIcon": true, "type": "numberentry", "correctAnswerStyle": "plain", "precisionPartialCredit": "50", "variableReplacements": [], "allowFractions": false, "customName": "", "minValue": "cc", "notationStyles": ["plain", "en", "si-en"], "mustBeReduced": false, "correctAnswerFraction": false, "showCorrectAnswer": true, "unitTests": [], "mustBeReducedPC": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "prompt": "<p>What is the y-intercept of $f(x)$?</p>", "variableReplacementStrategy": "originalfirst", "precisionMessage": "You have not given your answer to the correct precision.", "useCustomName": false, "precisionType": "dp", "strictPrecision": false, "adaptiveMarkingPenalty": 0, "precision": "3", "maxValue": "cc", "marks": 1, "showPrecisionHint": true, "scripts": {}}, {"shuffleChoices": true, "showFeedbackIcon": true, "type": "m_n_x", "answers": ["INCREASING", "DECREASING"], "maxAnswers": 0, "variableReplacements": [], "minAnswers": 0, "customName": "", "showCorrectAnswer": true, "shuffleAnswers": true, "unitTests": [], "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "prompt": "<p>Determine on what intervals $f(x)$ is increasing and decreasing.&nbsp;<em> </em></p>\n<p><em>Match only one CHOICE to each ANSWER.</em></p>", "layout": {"type": "all", "expression": ""}, "variableReplacementStrategy": "originalfirst", "useCustomName": false, "showCellAnswerState": true, "matrix": [[0, 0], [0, "1"], [0, 0], ["1", 0]], "maxMarks": "2", "displayType": "radiogroup", "minMarks": "2", "choices": ["$(-\\infty,\\var{reLeft})$", "$(\\var{reLeft},\\var{reRight})$", "$(\\var{reRight},+\\infty)$", "$(-\\infty,\\var{reLeft}) \\cup (\\var{reRight},+\\infty)$"], "marks": 0, "scripts": {}, "adaptiveMarkingPenalty": 0, "warningType": "none"}, {"showFeedbackIcon": true, "type": "jme", "prompt": "<p>Where is the relative maximum of $f(x)$.</p>\n<p><em>Express your answer in the format:&nbsp;<strong></strong><strong>vector(x,y)</strong></em></p>", "showPreview": true, "variableReplacements": [], "vsetRangePoints": 5, "failureRate": 1, "customName": "", "answer": "vector({max[0]},{max[1]})", "showCorrectAnswer": true, "unitTests": [], "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "vsetRange": [0, 1], "variableReplacementStrategy": "originalfirst", "valuegenerators": [], "useCustomName": false, "checkingType": "absdiff", "adaptiveMarkingPenalty": 0, "checkingAccuracy": 0.001, "marks": 1, "scripts": {}, "checkVariableNames": false}, {"showFeedbackIcon": true, "type": "jme", "prompt": "<p>Where is the relative minimum of $f(x)$.</p>\n<p><em>Express your answer in the format:&nbsp;<strong></strong><strong>vector(x,y)</strong></em></p>", "showPreview": true, "variableReplacements": [], "vsetRangePoints": 5, "failureRate": 1, "customName": "", "answer": "vector({min[0]},{min[1]})", "showCorrectAnswer": true, "unitTests": [], "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "vsetRange": [0, 1], "variableReplacementStrategy": "originalfirst", "valuegenerators": [], "useCustomName": false, "checkingType": "absdiff", "adaptiveMarkingPenalty": 0, "checkingAccuracy": 0.001, "marks": 1, "scripts": {}, "checkVariableNames": false}, {"showFeedbackIcon": true, "type": "numberentry", "correctAnswerStyle": "plain", "precisionPartialCredit": "50", "variableReplacements": [], "allowFractions": false, "customName": "", "minValue": "{fofXval}", "notationStyles": ["plain", "en", "si-en"], "mustBeReduced": false, "correctAnswerFraction": false, "showCorrectAnswer": true, "unitTests": [], "mustBeReducedPC": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "prompt": "<p>Find the value of $f(\\var{xval})$ to the nearest thousandths.</p>", "variableReplacementStrategy": "originalfirst", "precisionMessage": "You have not given your answer to the correct precision.", "useCustomName": false, "precisionType": "dp", "strictPrecision": false, "adaptiveMarkingPenalty": 0, "precision": "3", "maxValue": "{fofXval}", "marks": 1, "showPrecisionHint": false, "scripts": {}}, {"shuffleChoices": true, "showFeedbackIcon": true, "type": "m_n_x", "answers": ["DOMAIN", "RANGE"], "maxAnswers": "2", "variableReplacements": [], "minAnswers": "0", "customName": "", "showCorrectAnswer": true, "shuffleAnswers": false, "unitTests": [], "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "prompt": "<p>What is the domain and range of the function, $f(x)$?</p>", "layout": {"type": "all", "expression": ""}, "variableReplacementStrategy": "originalfirst", "useCustomName": false, "showCellAnswerState": true, "matrix": [["1", "1"], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0]], "maxMarks": "2", "displayType": "checkbox", "minMarks": "0", "choices": ["$(-\\infty,+\\infty)$", "$(-\\infty,\\var{reLeft}]$", "$(-\\infty,\\var{reRight}]$", "$[-\\infty,+\\infty]$", "$[\\var{reLeft},+\\infty)$", "$[\\var{reRight},+\\infty)$", "$[\\var{reLeft},\\var{reRight}]$", "$(-\\infty,\\var{max[1]}]$", "$[\\var{min[1]},+\\infty)$", "$[\\var{min[1]},\\var{max[1]}]$"], "marks": 0, "scripts": {}, "adaptiveMarkingPenalty": 0, "warningType": "warn"}], "statement": "<p>Given the function below:</p>\n<p>$f(x)=\\simplify{x^3+{cx2}x^2+{cx}x+{cc}}$</p>", "contributors": [{"name": "Terry Young", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3130/"}]}]}], "contributors": [{"name": "Terry Young", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3130/"}]}