// Numbas version: exam_results_page_options
{"name": "Maria'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": [{"parts": [{"type": "gapfill", "variableReplacements": [], "useCustomName": false, "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "sortAnswers": false, "customName": "", "variableReplacementStrategy": "originalfirst", "extendBaseMarkingAlgorithm": true, "scripts": {}, "showFeedbackIcon": true, "showCorrectAnswer": true, "unitTests": [], "gaps": [{"type": "numberentry", "variableReplacements": [], "mustBeReducedPC": 0, "useCustomName": false, "adaptiveMarkingPenalty": 0, "correctAnswerStyle": "plain", "mustBeReduced": false, "maxValue": "0", "showFeedbackIcon": true, "allowFractions": false, "unitTests": [], "notationStyles": ["plain", "en", "si-en"], "showFractionHint": true, "customMarkingAlgorithm": "", "correctAnswerFraction": false, "customName": "", "variableReplacementStrategy": "originalfirst", "extendBaseMarkingAlgorithm": true, "scripts": {}, "showCorrectAnswer": true, "marks": 1, "minValue": "0"}], "marks": 0, "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>"}, {"type": "gapfill", "variableReplacements": [], "useCustomName": false, "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "sortAnswers": false, "customName": "", "variableReplacementStrategy": "originalfirst", "extendBaseMarkingAlgorithm": true, "scripts": {}, "showFeedbackIcon": true, "showCorrectAnswer": true, "unitTests": [], "gaps": [{"type": "numberentry", "variableReplacements": [], "mustBeReducedPC": 0, "useCustomName": false, "adaptiveMarkingPenalty": 0, "correctAnswerStyle": "plain", "mustBeReduced": false, "maxValue": "{length(c)}", "showFeedbackIcon": true, "allowFractions": false, "unitTests": [], "notationStyles": ["plain", "en", "si-en"], "showFractionHint": true, "customMarkingAlgorithm": "", "correctAnswerFraction": false, "customName": "", "variableReplacementStrategy": "originalfirst", "extendBaseMarkingAlgorithm": true, "scripts": {}, "showCorrectAnswer": true, "marks": 1, "minValue": "{length(c)}"}, {"type": "jme", "showPreview": true, "checkVariableNames": false, "useCustomName": false, "adaptiveMarkingPenalty": 0, "vsetRange": [0, 1], "checkingAccuracy": 0.001, "checkingType": "absdiff", "showFeedbackIcon": true, "valuegenerators": [], "variableReplacements": [], "unitTests": [], "customMarkingAlgorithm": "", "vsetRangePoints": 5, "answer": "{set_of_holes}", "customName": "", "variableReplacementStrategy": "originalfirst", "extendBaseMarkingAlgorithm": true, "scripts": {}, "showCorrectAnswer": true, "marks": 1, "failureRate": 1}], "marks": 0, "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>"}], "functions": {}, "tags": [], "preamble": {"js": "", "css": ""}, "name": "Maria's copy of Domain of a rational function", "variables": {"set_of_holes": {"description": "", "definition": "set(c)", "group": "Ungrouped variables", "templateType": "anything", "name": "set_of_holes"}, "num": {"description": "", "definition": "[random(-12..12),random(-12..12 except 0)]", "group": "Ungrouped variables", "templateType": "anything", "name": "num"}, "rat": {"description": "", "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", "group": "Ungrouped variables", "templateType": "anything", "name": "rat"}, "n": {"description": "", "definition": "random(2..4)", "group": "Ungrouped variables", "templateType": "anything", "name": "n"}, "c": {"description": "", "definition": "sort(shuffle(-12..12)[0..n])", "group": "Ungrouped variables", "templateType": "anything", "name": "c"}, "b": {"description": "", "definition": "a+random(1..12)", "group": "Ungrouped variables", "templateType": "anything", "name": "b"}, "a": {"description": "", "definition": "random(-12..-1)", "group": "Ungrouped variables", "templateType": "anything", "name": "a"}, "inp": {"description": "", "definition": "expression(random('x','r','s','t','w'))", "group": "Ungrouped variables", "templateType": "anything", "name": "inp"}, "out": {"description": "", "definition": "expression(random('f','h','g','p','q','y'))", "group": "Ungrouped variables", "templateType": "anything", "name": "out"}}, "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": {}, "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"}, "variable_groups": [], "variablesTest": {"condition": "", "maxRuns": 100}, "statement": "<p>Given the real functions below, you should be able to determine their domains.&nbsp;</p>", "extensions": [], "ungrouped_variables": ["out", "inp", "num", "n", "c", "rat", "a", "b", "set_of_holes"], "contributors": [{"name": "Ben Brawn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/605/"}, {"name": "Maria Aneiros", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3388/"}]}]}], "contributors": [{"name": "Ben Brawn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/605/"}, {"name": "Maria Aneiros", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3388/"}]}