// Numbas version: finer_feedback_settings
{"name": "JD's copy of Polynomial Graph 1", "extensions": ["geogebra"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"functions": {"graph": {"language": "jme", "definition": "geogebra_applet('https://ggbm.at/aXxv2ECN', defs, [])", "type": "html", "parameters": []}}, "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"}, "preamble": {"css": "", "js": ""}, "variables": {"a": {"group": "Ungrouped variables", "templateType": "anything", "definition": "random(-3..3#0.5)", "name": "a", "description": ""}, "y2": {"group": "Ungrouped variables", "templateType": "anything", "definition": "n*((-b)^3)/3 + 0.5*(a+b)*(-b)^2+(a*b)*(-b)+c", "name": "y2", "description": "<p>y2</p>"}, "b": {"group": "Ungrouped variables", "templateType": "anything", "definition": "random(-3..3#0.5)", "name": "b", "description": ""}, "n": {"group": "Ungrouped variables", "templateType": "anything", "definition": "random(-1,1)", "name": "n", "description": ""}, "D": {"group": "Ungrouped variables", "templateType": "anything", "definition": "(a+b)^2 - 4*a*b*n", "name": "D", "description": ""}, "c": {"group": "Ungrouped variables", "templateType": "anything", "definition": "random(-3..3#0.5)", "name": "c", "description": ""}, "y1": {"group": "Ungrouped variables", "templateType": "anything", "definition": "n*((-a)^3)/3 + 0.5*(a+b)*(-a)^2+(a*b)*(-a)+c", "name": "y1", "description": ""}, "defs": {"group": "Ungrouped variables", "templateType": "anything", "definition": "[\n  ['a',a],\n  ['b',b],\n  ['c',c],\n  ['n',n]\n]", "name": "defs", "description": ""}}, "variable_groups": [], "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>", "tags": [], "rulesets": {}, "name": "JD's copy of Polynomial Graph 1", "ungrouped_variables": ["a", "b", "c", "defs", "D", "n", "y1", "y2"], "variablesTest": {"condition": "a<>b and abs(b-a)>1 and abs(y1)<10 and abs(y2)<10 and D>0", "maxRuns": "200"}, "parts": [{"matrix": ["-1", "1", "-1", "1", "-1", "-1", "1"], "scripts": {}, "marks": 0, "distractors": ["", "", "", "", "", "", ""], "maxAnswers": 0, "warningType": "none", "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "maxMarks": 0, "minMarks": 0, "minAnswers": "2", "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>"], "variableReplacements": [], "shuffleChoices": true, "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>", "showFeedbackIcon": true, "displayType": "checkbox", "type": "m_n_2", "displayColumns": 0}], "extensions": ["geogebra"], "type": "question", "contributors": [{"name": "Adrian Jannetta", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/164/"}, {"name": "JD Ichwan", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3389/"}]}]}], "contributors": [{"name": "Adrian Jannetta", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/164/"}, {"name": "JD Ichwan", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3389/"}]}