// Numbas version: exam_results_page_options
{"name": "Ugur's copy of Domain of a rational function", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Ugur's copy of Domain of a rational function", "tags": [], "metadata": {"description": "<p>Given a randomised rational function&nbsp;select the possible ways of writing the domain of the function.</p>", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "<p>Given the real functions below, you should be able to determine their domains.&nbsp;</p>", "advice": "<p></p>\n<p><g class=\"gr_ gr_20 gr-alert gr_gramm gr_inline_cards gr_run_anim Grammar multiReplace\" id=\"20\" data-gr-id=\"20\">Division</g> is defined for all real numbers except zero. So when a function involves division (such as a rational function), any input that will result in a division by zero is not allowed. Rational functions are simply a fraction/division of polynomials, so&nbsp;the only real numbers that are not in the domain of a rational function are the roots of the polynomial in the denominator. Sometimes, (for example part c above) you will need to factorise the denominator to determine its roots.</p>\n<p></p>\n<p>d) Even though 'something divided by itself is 1' division by zero is still undefined. So the domain of $h$ is not all of $\\mathbb{R}$, the domain does not include the number $\\var{c[0]}$. In other words, $h(\\var{c[0]})$ is undefined but for all other $r$, $h(r)=1$.</p>", "rulesets": {}, "extensions": [], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"a": {"name": "a", "group": "Ungrouped variables", "definition": "random(-12..-1)", "description": "", "templateType": "anything", "can_override": false}, "inp": {"name": "inp", "group": "Ungrouped variables", "definition": "expression(random('x','r','s','t','w'))", "description": "", "templateType": "anything", "can_override": false}, "set_of_holes": {"name": "set_of_holes", "group": "Ungrouped variables", "definition": "set(c)", "description": "", "templateType": "anything", "can_override": false}, "out": {"name": "out", "group": "Ungrouped variables", "definition": "expression(random('f','h','g','p','q','y'))", "description": "", "templateType": "anything", "can_override": false}, "b": {"name": "b", "group": "Ungrouped variables", "definition": "a+random(1..12)", "description": "", "templateType": "anything", "can_override": false}, "n": {"name": "n", "group": "Ungrouped variables", "definition": "random(2..4)", "description": "", "templateType": "anything", "can_override": false}, "num": {"name": "num", "group": "Ungrouped variables", "definition": "[random(-12..12),random(-12..12 except 0)]", "description": "", "templateType": "anything", "can_override": false}, "c": {"name": "c", "group": "Ungrouped variables", "definition": "sort(shuffle(-12..12)[0..n])", "description": "", "templateType": "anything", "can_override": false}, "rat": {"name": "rat", "group": "Ungrouped variables", "definition": "if(n=3,'\\\\[\\\\simplify{{out}({inp})=({num[0]}{inp}+{num[1]})/(({inp}-{c[0]})({inp}-{c[1]})*({inp}-{c[2]}))}\\\\]',\nif(n=2,'\\\\[\\\\simplify{{out}({inp})=({num[0]}{inp}+{num[1]})/(({inp}-{c[0]})({inp}-{c[1]}))}\\\\]',\n'\\\\[\\\\simplify{{out}({inp})=({num[0]}{inp}+{num[1]})/(({inp}-{c[0]})({inp}-{c[1]})*({inp}-{c[2]})*({inp}-{c[3]}))}\\\\]'))\n    \n  \n", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["out", "inp", "num", "n", "c", "rat", "a", "b", "set_of_holes"], "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>There is a single real number that is not in the domain of the function&nbsp;</p>\n<p>\\[f(x)=\\frac{1}{x}.\\]</p>\n<p>That number&nbsp;is&nbsp;[[0]].&nbsp;</p>", "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "0", "maxValue": "0", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "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>There are&nbsp;[[0]]&nbsp;real numbers that are not in the domain&nbsp;of&nbsp;{rat} these are&nbsp;[[1]].</p>\n<p><strong>Note:&nbsp;</strong>If the numbers were $-2,1$ and $4$ you would enter&nbsp;<strong>set(-2,1,4)</strong></p>", "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "{length(c)}", "maxValue": "{length(c)}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "jme", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "{set_of_holes}", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": []}], "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, "prompt": "<p>Which of the following represents the domain of \\[\\simplify{g(x)=(x^2-{c[0]+c[1]}x+{c[0]*c[1]})/(x^2-{a+b}x+{a*b})} \\ ?\\]</p>\n<p>(There could be more than one correct choice).</p>", "minMarks": 0, "maxMarks": 0, "shuffleChoices": true, "displayType": "checkbox", "displayColumns": "1", "minAnswers": 0, "maxAnswers": 0, "warningType": "none", "showCellAnswerState": true, "markingMethod": "sum ticked cells", "choices": ["<p>$\\mathbb{R}$</p>", "<p>$\\{x\\in \\mathbb{R}:\\,\\var{a+b}&lt;x&lt;\\var{a*b}\\}$</p>", "<p>$\\{x\\in \\mathbb{R}:\\,x\\ne \\var{c[0]},\\var{c[1]}\\}$</p>", "<p>$\\{x\\in \\mathbb{R}:\\,x\\ne \\var{a},\\var{b}\\}$</p>", "<p>$\\mathbb{R}\\setminus \\{\\var{a},\\var{b}\\}$</p>", "<p>$\\mathbb{R}\\setminus \\{\\var{c[0]},\\var{c[1]}\\}$</p>", "<p>$\\{x\\in \\mathbb{R}:\\,x\\ne \\var{-a},\\var{-b}\\}$</p>"], "matrix": [0, 0, 0, "1", "1", 0, 0], "distractors": ["", "", "", "", "", "", ""]}, {"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, "prompt": "<p>Which of the following is the domain of</p>\n<p>\\[h(r)=\\simplify{(r-{c[0]})/(r-{c[0]})}?\\]</p>", "minMarks": 0, "maxMarks": 0, "shuffleChoices": false, "displayType": "radiogroup", "displayColumns": "1", "showCellAnswerState": true, "choices": ["<p>$\\{r\\in\\mathbb{R}:\\,r\\ne \\var{c[0]}\\}$</p>", "<p>$\\mathbb{R}$</p>"], "matrix": ["0", "1"], "distractors": ["", ""]}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "contributors": [{"name": "Ben Brawn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/605/"}, {"name": "Ugur Efem", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/14200/"}]}]}], "contributors": [{"name": "Ben Brawn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/605/"}, {"name": "Ugur Efem", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/14200/"}]}