// Numbas version: exam_results_page_options
{"name": "Polynomial Graph 1", "extensions": ["geogebra"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Polynomial Graph 1", "tags": [], "metadata": {"description": "<p>This uses an embedded Geogebra graph of a cubic polynomial with random coefficients set by NUMBAS.&nbsp; Student has to decide what kind of map it represents and whether an inverse function exists.</p>", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "<p>Select the true statements about the following graph.</p>\n<p>{geogebra_applet('https://ggbm.at/aXxv2ECN', defs, [])}</p>", "advice": "<p><strong>This is a function</strong>.&nbsp; The graph passes the vertical line test, because a vertical line would touch only one point on the curve.&nbsp; That means each input ($x$-axis, domain) goes to one output ($y$-axis, range).</p>\n<p><strong>This is a many-to-one map</strong>.&nbsp; Some of the range values can be obtained from different domain values.</p>\n<p>This function <strong>does not have an inverse function</strong>.&nbsp; The graph fails the horizontal line test, because a horizontal line would make contact with more than one point on the curve.</p>", "rulesets": {}, "extensions": ["geogebra"], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"b": {"name": "b", "group": "Ungrouped variables", "definition": "random(-3..3#0.5)", "description": "", "templateType": "anything", "can_override": false}, "y2": {"name": "y2", "group": "Ungrouped variables", "definition": "n*((-b)^3)/3 + 0.5*(a+b)*(-b)^2+(a*b)*(-b)+c", "description": "<p>y2</p>", "templateType": "anything", "can_override": false}, "D": {"name": "D", "group": "Ungrouped variables", "definition": "(a+b)^2 - 4*a*b*n", "description": "", "templateType": "anything", "can_override": false}, "a": {"name": "a", "group": "Ungrouped variables", "definition": "random(-3..3#0.5)", "description": "", "templateType": "anything", "can_override": false}, "defs": {"name": "defs", "group": "Ungrouped variables", "definition": "[\n  ['a',a],\n  ['b',b],\n  ['c',c],\n  ['n',n]\n]", "description": "", "templateType": "anything", "can_override": false}, "c": {"name": "c", "group": "Ungrouped variables", "definition": "random(-3..3#0.5)", "description": "", "templateType": "anything", "can_override": false}, "y1": {"name": "y1", "group": "Ungrouped variables", "definition": "n*((-a)^3)/3 + 0.5*(a+b)*(-a)^2+(a*b)*(-a)+c", "description": "", "templateType": "anything", "can_override": false}, "n": {"name": "n", "group": "Ungrouped variables", "definition": "random(-1,1)", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "a<>b and abs(b-a)>1 and abs(y1)<10 and abs(y2)<10 and D>0", "maxRuns": "200"}, "ungrouped_variables": ["a", "b", "c", "defs", "D", "n", "y1", "y2"], "variable_groups": [], "functions": {"graph": {"parameters": [], "type": "html", "language": "jme", "definition": "geogebra_applet('https://ggbm.at/aXxv2ECN', defs, [])"}}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "m_n_2", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<ul>\n<li>You may select more than one option.</li>\n<li>You can assume the visible graph represents the entire curve</li>\n</ul>", "minMarks": 0, "maxMarks": 0, "shuffleChoices": true, "displayType": "checkbox", "displayColumns": 0, "minAnswers": "2", "maxAnswers": 0, "warningType": "none", "showCellAnswerState": true, "markingMethod": "sum ticked cells", "choices": ["<p>One-to-one map</p>", "<p>Many-to-one map</p>", "<p>One-to-many map</p>", "<p>This graph is a function.</p>", "<p>This graph is&nbsp;<strong><em>not</em>&nbsp;&nbsp;</strong>a function.</p>", "<p>Inverse function exists.</p>", "<p>Inverse function <em><strong>does not</strong></em> exist.</p>"], "matrix": ["-1", "1", "-1", "1", "-1", "-1", "1"], "distractors": ["", "", "", "", "", "", ""]}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "contributors": [{"name": "Adrian Jannetta", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/164/"}]}]}], "contributors": [{"name": "Adrian Jannetta", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/164/"}]}