// Numbas version: exam_results_page_options
{"name": "Weitere \u00dcbungen (Lektion 4)", "metadata": {"description": "<p>&Uuml;bungen zu&nbsp;Relationen und Funktionen</p>", "licence": "Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International"}, "duration": 0, "percentPass": "0", "showQuestionGroupNames": false, "showstudentname": true, "question_groups": [{"name": "Group", "pickingStrategy": "all-ordered", "pickQuestions": 1, "questionNames": ["", ""], "questions": [{"name": "Relationen und deren Eigenschaften", "extensions": ["geogebra"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Andreas Vohns", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3622/"}], "tags": [], "metadata": {"description": "<p>Untersuchung von Relationen</p>", "licence": "Creative Commons Attribution-ShareAlike 4.0 International"}, "statement": "<p>Auf $\\mathbb{N}\\times\\mathbb{N}$ betrachten wir&nbsp;zwei Relationen $x\\mathbf{R}y$, deren Graphen im Bereich $x,y\\leq 12$&nbsp;so ausschauen:</p>\n<p><em><strong>Beachten Sie:</strong> Anders als auf den Folien ist hier $x\\mathbf{R}y$ und <strong>nicht</strong> $y\\mathbf{R}x$&nbsp; dargestellt. <br/>Bitte etwas Geduld beim Laden der Graphen.</em></p>\n<table>\n<tbody>\n<tr>\n<td style=\"text-align: center;\">\n<h4>&nbsp;A</h4>\n</td>\n<td style=\"text-align: center;\">\n<h4>&nbsp;B</h4>\n</td>\n</tr>\n<tr>\n<td style=\"text-align: center;\">{apps[0]}</td>\n<td style=\"text-align: center;\">{apps[1]}</td>\n</tr>\n</tbody>\n</table>", "advice": "<p><strong>Zu Aufgabenteil a): </strong></p>\n<p>Die L&ouml;sung findet man durch &Uuml;berpr&uuml;fen der Werte einzelner Zahlenpaare $(x\\mid y)$, die in der Relation enthalten sein sollten oder nicht und bei denen man dann schaut, ob die entsprechenden Punkte in den Graphen enthalten sind oder nicht.</p>\n<p><strong>Zu Aufgabenteil b):</strong></p>\n<p><em>(i) Reflexivit&auml;t:</em></p>\n<p>reflexiv: Alle Punkte der Diagonalen m&uuml;ssen markiert sein.</p>\n<p>irreflexiv: Kein Punkt der Diagonalen darf markiert sein.</p>\n<p>weder reflexiv, noch irreflexiv: es gibt Punkte auf der Diagonalen, die markiert sind und solche, wo das nicht der Fall ist.</p>\n<p><em>(ii) Symmetrie</em></p>\n<p>symmetrisch:&nbsp;Alle Punkte auf oder unterhalb von $y=x$ haben Spiegelunkte an $y=x$ auf oder unterhalb der Geraden (und umgekehrt).</p>\n<p>antisymmetrisch: Das stimmt zwar nicht, aber&nbsp;alle Punkte auf der Geraden $y=x$ sind markiert.</p>\n<p>asymmetrisch:&nbsp;selbst&nbsp;das, was bei antisymmetrisch steht, ist nicht richtig.</p>", "rulesets": {}, "variables": {"a": {"name": "a", "group": "Listen", "definition": "distinct(a1+a2)", "description": "", "templateType": "anything"}, "Auswahl": {"name": "Auswahl", "group": "Relationen", "definition": "[\"gcd(x[0],x[1])<=\"+n,\"lcm(x[0],x[1])>=\"+m,\"mod(2*x[0]+3*x[1],\"+n+\")=mod(2*x[1]+3*x[0],\"+m+\")\",\"gcd(x[0],x[1])<>x[0]\",\"lcm(x[0],x[1])<x[0]*x[1]\",\"mod(x[0]-x[1],\"+n+\")=mod(x[1]-x[0],\"+n+\")\"]", "description": "", "templateType": "anything"}, "Graphs": {"name": "Graphs", "group": "Listen", "definition": "[filter(eval(expression(what[0])),x,a),filter(eval(expression(what[1])),x,a)]", "description": "", "templateType": "anything"}, "rando": {"name": "rando", "group": "Parameter", "definition": "deal(6)", "description": "", "templateType": "anything"}, "n": {"name": "n", "group": "Parameter", "definition": "random(3..6)", "description": "", "templateType": "anything"}, "m": {"name": "m", "group": "Parameter", "definition": "random(7..9)", "description": "", "templateType": "anything"}, "Auswahltex": {"name": "Auswahltex", "group": "Relationen", "definition": "[\"\\\\operatorname\\{ggT\\}(x,y)\\\\leq{n}\",\"\\\\operatorname\\{kgV\\}(x,y)\\\\geq{m}\",\"(2\\\\cdot x+3\\\\cdot y)\\\\mod {n}=(2\\\\cdot y + 3\\\\cdot x)\\\\mod {m}\",\"\\\\operatorname\\{ggT\\}(x,y)\\\\not=x\",\"\\\\operatorname\\{kgV\\}(x,y)&lt;x\\\\cdot y\",\"(x-y)\\\\equiv(y-x)\\\\pmod {n}\"]", "description": "", "templateType": "anything"}, "what": {"name": "what", "group": "Relationen", "definition": "[Auswahl[rando[0]],Auswahl[rando[1]],Auswahl[rando[2]],Auswahl[rando[3]],Auswahl[rando[4]],Auswahl[rando[5]]]", "description": "", "templateType": "anything"}, "GraphsAsVectors": {"name": "GraphsAsVectors", "group": "Listen", "definition": "[map(vector(x[0],x[1]),x,Graphs[0]),map(vector(x[0],x[1]),x,Graphs[1])]", "description": "", "templateType": "anything"}, "defs": {"name": "defs", "group": "Listen", "definition": "[dict(map([\"P_{\"+100*x[0]+x[1]+\"}\",vector(x[0],x[1])],x,GraphsAsVectors[0])),dict(map([\"P_{\"+100*x[0]+x[1]+\"}\",vector(x[0],x[1])],x,GraphsAsVectors[1]))]", "description": "", "templateType": "anything"}, "apps": {"name": "apps", "group": "Listen", "definition": "[geogebra_applet('https://www.geogebra.org/m/wgr65rt6',defs[0]),geogebra_applet('https://www.geogebra.org/m/wgr65rt6',defs[1])]", "description": "", "templateType": "anything"}, "test": {"name": "test", "group": "Relationen", "definition": "Auswahl[5]", "description": "", "templateType": "anything"}, "Test1": {"name": "Test1", "group": "Ungrouped variables", "definition": "mod(2+3,2)", "description": "", "templateType": "anything"}, "Test2": {"name": "Test2", "group": "Ungrouped variables", "definition": "mod(3+2,2)", "description": "", "templateType": "anything"}, "Tester": {"name": "Tester", "group": "Ungrouped variables", "definition": "Test1=Test2", "description": "", "templateType": "anything"}, "a2": {"name": "a2", "group": "Listen", "definition": "map([x[1],x[0]],x,a1)", "description": "", "templateType": "anything"}, "a1": {"name": "a1", "group": "Listen", "definition": "combinations_with_replacement(sort(deal(13))[1..13],2)", "description": "", "templateType": "anything"}, "reflex": {"name": "reflex", "group": "Relationen", "definition": "[[0,0,1],[0,0,1],[0,0,1],[0,1,0],[1,0,0],[1,0,0]]", "description": "", "templateType": "anything"}, "sym": {"name": "sym", "group": "Relationen", "definition": "[[1,0,0],[1,0,0],[0,1,0],[0,1,0],[0,1,0],[1,0,0]]", "description": "", "templateType": "anything"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["Test1", "Test2", "Tester"], "variable_groups": [{"name": "Listen", "variables": ["a", "Graphs", "GraphsAsVectors", "defs", "apps", "a2", "a1"]}, {"name": "Relationen", "variables": ["Auswahl", "Auswahltex", "what", "test", "reflex", "sym"]}, {"name": "Parameter", "variables": ["rando", "n", "m"]}], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "m_n_x", "useCustomName": true, "customName": "Relation identifizieren", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [{"label": "Eigenschaften untersuchen", "rawLabel": "", "otherPart": 1, "variableReplacements": [], "availabilityCondition": "", "penalty": "", "penaltyAmount": 0, "lockAfterLeaving": false}], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": "Relationen erkannt", "prompt": "<p><strong>Aufgabenstellung:</strong></p>\n<p>Kreuzen&nbsp;Sie f&uuml;r&nbsp;die beiden Graphen (A, B) jeweils&nbsp;die zugeh&ouml;rige&nbsp;Definition der Relation an (es gibt genau zwei richtige Antworten)!</p>", "minMarks": 0, "maxMarks": 0, "minAnswers": "0", "maxAnswers": "2", "shuffleChoices": true, "shuffleAnswers": false, "displayType": "checkbox", "warningType": "prevent", "showCellAnswerState": true, "choices": ["$x{\\mathbf{R}}y :\\Leftrightarrow$ {latex(Auswahltex[rando[0]])}", "$x{\\mathbf{R}}y :\\Leftrightarrow$ {latex(Auswahltex[rando[1]])}", "$x{\\mathbf{R}}y :\\Leftrightarrow$ {latex(Auswahltex[rando[2]])}", "$x{\\mathbf{R}}y :\\Leftrightarrow$ {latex(Auswahltex[rando[3]])}", "$x{\\mathbf{R}}y :\\Leftrightarrow$ {latex(Auswahltex[rando[4]])}", "$x{\\mathbf{R}}y :\\Leftrightarrow$ {latex(Auswahltex[rando[5]])}"], "matrix": [["2", "-1"], ["-1", "2"], ["-1", "-1"], ["-1", "-1"], ["-1", "-1"], ["-1", "-1"]], "layout": {"type": "all", "expression": ""}, "answers": ["Graph A", "Graph B"]}, {"type": "gapfill", "useCustomName": true, "customName": "Eigenschaften untersuchen", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": "Eigenschaften erkannt", "prompt": "<p><strong>Aufgabenstellung:</strong></p>\n<p><em>Ermitteln Sie anhand des Graphen oder der Defiinition&nbsp;die Eigenschaften der Relation!</em></p>\n<p>Die Relation <strong>A&nbsp;</strong>mit&nbsp;$x{\\mathbf{R}}y :\\Leftrightarrow$ {latex(Auswahltex[rando[0]])}</p>\n<ul>\n<li>ist [[0]];</li>\n<li>ist&nbsp;[[1]].</li>\n</ul>\n<p>Die Relation&nbsp;<strong>B&nbsp;</strong>mit&nbsp;$x{\\mathbf{R}}y :\\Leftrightarrow$ {latex(Auswahltex[rando[1]])}</p>\n<ul>\n<li>ist [[2]];&nbsp;</li>\n<li>ist [[3]].</li>\n</ul>", "gaps": [{"type": "1_n_2", "useCustomName": true, "customName": "reflexivA", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minMarks": 0, "maxMarks": 0, "shuffleChoices": false, "displayType": "dropdownlist", "displayColumns": "1", "showCellAnswerState": true, "choices": ["reflexiv", "irreflexiv", "weder reflexiv, noch irreflexiv"], "matrix": "reflex[rando[0]]"}, {"type": "1_n_2", "useCustomName": true, "customName": "symmetrieA", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minMarks": 0, "maxMarks": 0, "shuffleChoices": false, "displayType": "dropdownlist", "displayColumns": "1", "showCellAnswerState": true, "choices": ["symmetrisch", "asymmetrisch", "antisymmetrisch"], "matrix": "sym[rando[0]]"}, {"type": "1_n_2", "useCustomName": true, "customName": "reflexivB", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minMarks": 0, "maxMarks": 0, "shuffleChoices": false, "displayType": "dropdownlist", "displayColumns": "1", "showCellAnswerState": true, "choices": ["reflexiv", "irreflexiv", "weder reflexiv, noch irreflexiv"], "matrix": "reflex[rando[1]]"}, {"type": "1_n_2", "useCustomName": true, "customName": "symmetrieB", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minMarks": 0, "maxMarks": 0, "shuffleChoices": false, "displayType": "dropdownlist", "displayColumns": "1", "showCellAnswerState": true, "choices": ["symmetrisch", "asymmetrisch", "antisymmetrisch"], "matrix": "sym[rando[1]]"}], "sortAnswers": false}], "partsMode": "explore", "maxMarks": 0, "objectives": [{"name": "Relationen erkannt", "limit": "4", "mode": "sum"}, {"name": "Eigenschaften erkannt", "limit": "4", "mode": "sum"}], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "when-active"}, {"name": "Eigenschaften von Funktionen", "extensions": ["geogebra"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Andreas Vohns", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3622/"}], "tags": [], "metadata": {"description": "<p>Injektiv, Surjektiv, Bijektiv mit parametrisierten Funktionsgraphen.</p>", "licence": "Creative Commons Attribution-ShareAlike 4.0 International"}, "statement": "<p>Gegeben ist folgende Zuordnung: $f:A \\to B$ mit $x\\mapsto \\var[fractionNumbers]{1/p}x^\\var{n}+\\var[fractionNumbers]{(1 + o/10)} x$ f&uuml;r alle $x\\in A$.</p>\n<p>Ihr Graph schaut im Bereich $-20\\leq x\\leq 20$ so aus:</p>\n<p>{graph}</p>\n<p><em>W&auml;hlen Sie im folgenden die Bedingungen so aus, dass die gew&uuml;nschte Eigenschaft der Zuordnung erf&uuml;llt ist!</em></p>", "advice": "<p>a) Da die Zuordnung f&uuml;r $A=\\mathbb{R}^+_0$ ausschlie&szlig;lich nicht-negative Funktionswerte annimmt, muss man hier $B=\\mathbb{R}^-$ ausw&auml;hlen, weil man dann sicher $X$ findet, denen kein $f(x)$ zugeordnet ist (das gilt sogar f&uuml;r alle $x\\in A$.</p>\n<p>b) F&uuml;r $A=\\mathbb{R}^+_0$ und $B=\\mathbb{R}$ schneiden f&uuml;r&nbsp;nicht negative $c$&nbsp;alle Geraden $y=c$ den Graphen der Zuordnung {if(n=3,\"genau&nbsp;einmal\",\"zweimal\")}, die Funktion ist also {if(n=3,\"injektiv\",\"nicht injektiv\")}.</p>\n<p>F&uuml;r $A=\\mathbb{R}^+_0$ und $B=\\mathbb{R}^+_0$ schneiden f&uuml;r&nbsp;nicht negative $c$&nbsp;alle Geraden $y=c$ den Graphen der Zuordnung genau einmal, die Funktion ist also injektiv.</p>\n<p>F&uuml;r $A=\\mathbb{R}^+_0$ und $B=\\mathbb{R}^-0$ ist die Zuordnung $f$ gar keine Funktion, also auch&nbsp;keine injektive Funktion (siehe Aufgabenteil a)).</p>\n<p>c) F&uuml;r&nbsp;$A=\\mathbb{R}, B=\\mathbb{R}$ schneiden&nbsp;{if(n=3,\"f&uuml;r alle\",\"f&uuml;r nicht alle negativen\")}&nbsp;$c$&nbsp;alle Geraden $y=c$ den Graphen der Zuordnung&nbsp;{if(n=3,\"genau einmal\",\"mindestens einmal\")}, daher ist die Funktion&nbsp;{if(n=3,\"bijektiv\",\"nicht bijektiv\")}.</p>\n<p>F&uuml;r&nbsp;$A=\\mathbb{R}, B=\\mathbb{R}^+_0$ schneiden&nbsp;f&uuml;r positive $c$&nbsp;alle Geraden $y=c$ den Graphen der Zuordnung&nbsp;{if(n=3,\"genau einmal\",\"zweimal\")}, daher ist die Funktion&nbsp;{if(n=3,\"bijektiv\",\"surjektiv, aber nicht injektiv\")}.</p>\n<p>F&uuml;r&nbsp;$A=\\mathbb{R}^+_0, B=\\mathbb{R}$ schneiden {if(n=3,\"f&uuml;r alle\",\"f&uuml;r alle negativen\")}&nbsp;$c$&nbsp;alle Geraden $y=c$ den Graphen der Zuordnung&nbsp;{if(n=3,\"genau einmal\",\"nicht\")}, daher ist die Funktion&nbsp;{if(n=3,\"bijektiv\",\"injektiv, aber nicht surjektiv\")}.</p>\n<p>F&uuml;r $A=\\mathbb{R}$ und $B=\\mathbb{R}^-$ ist die Zuordnung $f$ gar keine Funktion, weil man auch nicht-negative Zahlen als Funktionswerte ben&ouml;tigen w&uuml;rde.</p>", "rulesets": {}, "variables": {"n": {"name": "n", "group": "Ungrouped variables", "definition": "random(2..4)", "description": "", "templateType": "anything"}, "o": {"name": "o", "group": "Ungrouped variables", "definition": "random(3..7)", "description": "", "templateType": "anything"}, "p": {"name": "p", "group": "Ungrouped variables", "definition": "random(2..8)", "description": "", "templateType": "anything"}, "ggburl": {"name": "ggburl", "group": "Ungrouped variables", "definition": "'https://www.geogebra.org/m/gsj9uhtn'", "description": "", "templateType": "anything"}, "graph": {"name": "graph", "group": "Ungrouped variables", "definition": "geogebra_applet(ggburl,[[\"n\",n],[\"o\",o],[\"p\",p]])", "description": "", "templateType": "anything"}, "bloes": {"name": "bloes", "group": "Ungrouped variables", "definition": "[if(n=3,2,-2),2,if(n=3,-4,-2)]", "description": "", "templateType": "anything"}, "cloes": {"name": "cloes", "group": "Ungrouped variables", "definition": "[if(n=3,2,-2),if(n=3,-2,2),2,-2]", "description": "", "templateType": "anything"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["n", "o", "p", "ggburl", "graph", "bloes", "cloes"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "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": "<p>F&uuml;r $A=\\mathbb{R}_0^+$&nbsp;kann&nbsp;$B$ der folgende Zahlbereich sein, damit $f$ <strong>keine Funktion</strong> ist:</p>\n<p>[[0]]</p>", "gaps": [{"type": "1_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, "minMarks": 0, "maxMarks": 0, "shuffleChoices": true, "displayType": "radiogroup", "displayColumns": "0", "showCellAnswerState": false, "choices": ["$\\mathbb{R}$", "$\\mathbb{R}^+_0$", "$\\mathbb{R}^-$"], "matrix": [0, 0, "2"], "distractors": ["", "", ""]}], "sortAnswers": false}, {"type": "gapfill", "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": "<p>F&uuml;r $A=\\mathbb{R^+_0}$ ergeben folgende Zahlbereiche f&uuml;r $B$ eine <strong>injektive Funktion</strong>:</p>\n<p></p>\n<p>[[0]]</p>\n<p><em>Es k&ouml;nnen mehrere Auswahlen richtig sein!</em></p>", "gaps": [{"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, "minMarks": 0, "maxMarks": 0, "shuffleChoices": true, "displayType": "checkbox", "displayColumns": "0", "minAnswers": 0, "maxAnswers": 0, "warningType": "none", "showCellAnswerState": false, "choices": ["$\\mathbb{R}$", "$\\mathbb{R}^+_0$", "$\\mathbb{R}^-$"], "matrix": "bloes"}], "sortAnswers": false}, {"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, "minMarks": 0, "maxMarks": 0, "shuffleChoices": true, "displayType": "checkbox", "displayColumns": 0, "minAnswers": 0, "maxAnswers": 0, "warningType": "none", "showCellAnswerState": false, "choices": ["Die Zuordnung ist f&uuml;r $A=\\mathbb{R}, B=\\mathbb{R}$ eine&nbsp;<strong>bijektive Funktion</strong>.", "Die Zuordnung ist f&uuml;r $A=\\mathbb{R},B=\\mathbb{R^+_0}$ eine&nbsp;<strong>surjektive, nicht injektive&nbsp;Funktion</strong>.", "Die Zuordnung ist f&uuml;r $A=\\mathbb{R^+_0},B=\\mathbb{R}$ eine&nbsp;<strong>injektive, nicht&nbsp;surjektive&nbsp;Funktion</strong>.", "Die Zuordnung ist f&uuml;r $A=\\mathbb{R^-},B=\\mathbb{R}$ eine&nbsp;<strong>weder&nbsp;injektive,&nbsp;noch surjektive&nbsp;Funktion</strong>."], "matrix": "cloes"}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}]}], "allowPrinting": true, "navigation": {"allowregen": false, "reverse": true, "browse": true, "allowsteps": true, "showfrontpage": false, "showresultspage": "oncompletion", "navigatemode": "menu", "onleave": {"action": "none", "message": ""}, "preventleave": true, "startpassword": ""}, "timing": {"allowPause": true, "timeout": {"action": "none", "message": ""}, "timedwarning": {"action": "none", "message": ""}}, "feedback": {"showactualmark": true, "showtotalmark": true, "showanswerstate": true, "allowrevealanswer": true, "advicethreshold": 0, "intro": "", "reviewshowscore": true, "reviewshowfeedback": true, "reviewshowexpectedanswer": true, "reviewshowadvice": true, "feedbackmessages": []}, "contributors": [{"name": "Andreas Vohns", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3622/"}], "extensions": ["geogebra"], "custom_part_types": [], "resources": []}