// Numbas version: exam_results_page_options {"name": "Graph 3 (Inverse function?)", "extensions": ["geogebra"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Graph 3 (Inverse function?)", "tags": [], "metadata": {"description": "

This uses an embedded Geogebra graph of a cubic polynomial with random coefficients set by NUMBAS.  Student has to decide what kind of map it represents and whether an inverse function exists.

", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "

Select the true statements about the following graph.

\n

{geogebra_applet('https://ggbm.at/Bn7asVHR', defs, [])}

", "advice": "

This is not a function.  The graph fails the vertical line test, because a vertical line would usually touch two points on the curve.  

\n

This is a one-to-many map.  That means each input ($x$-axis, domain) often go to two outputs ($y$-axis, range).

\n

This relation does not have an inverse function.  Although it passes the horizontal line test....remember, the horizontal line test only applies to functions!

", "rulesets": {}, "extensions": ["geogebra"], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"defs": {"name": "defs", "group": "Ungrouped variables", "definition": "[\n ['b',b],\n ['c',c],\n ['n',n]\n]", "description": "", "templateType": "anything", "can_override": false}, "n": {"name": "n", "group": "Ungrouped variables", "definition": "random(-1,1)", "description": "", "templateType": "anything", "can_override": false}, "D": {"name": "D", "group": "Ungrouped variables", "definition": "b^2 - 4*c*n", "description": "", "templateType": "anything", "can_override": false}, "b": {"name": "b", "group": "Ungrouped variables", "definition": "random(-4..4#0.5)", "description": "", "templateType": "anything", "can_override": false}, "c": {"name": "c", "group": "Ungrouped variables", "definition": "random(-4..4#0.5)", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "D<0", "maxRuns": "200"}, "ungrouped_variables": ["b", "c", "defs", "D", "n"], "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": "", "minMarks": 0, "maxMarks": 0, "shuffleChoices": true, "displayType": "checkbox", "displayColumns": 0, "minAnswers": "2", "maxAnswers": 0, "warningType": "none", "showCellAnswerState": true, "markingMethod": "sum ticked cells", "choices": ["

One-to-one map

", "

Many-to-one map

", "

One-to-many map

", "

This graph is a function.

", "

This graph is not  a function.

", "

Inverse function exists.

", "

Inverse function does not exist.

"], "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/"}]}