// Numbas version: exam_results_page_options
{"name": "Joshua's copy of Domain of a piecewise function", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"extensions": [], "tags": [], "metadata": {"licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International", "description": "<p>Multiple choice <g class=\"gr_ gr_4 gr-alert gr_gramm gr_inline_cards gr_run_anim Grammar multiReplace\" id=\"4\" data-gr-id=\"4\">question</g>. Given a randomised polynomial select the possible ways of writing the domain of the function.</p>"}, "ungrouped_variables": ["a", "b", "c", "d", "b0", "b1", "b2", "Answer1", "Answer2", "Input1", "Input2"], "statement": "<p>Given the real function below, you should be able to determine its&nbsp;domain.&nbsp;</p>\n<p>$\\simplify{f}(\\simplify{t})=\\left\\{\\begin{align}&amp;\\simplify{0},&amp;&amp; \\text{ for } \\simplify{x}&lt; \\var{b0},&nbsp;\\\\&amp;\\simplify{{a}x+{b}},&amp;&amp; \\text{ for } \\var{b0}\\leq \\simplify{x}&lt; \\var{b1},\\\\ &amp;\\simplify{{c}x^2+{d}},&amp;&amp; \\text{ for } \\var{b1}\\leq\\simplify{x}&lt; \\var{b2},\\end{align}\\right.$</p>", "variablesTest": {"condition": "", "maxRuns": 100}, "variable_groups": [], "parts": [{"showCorrectAnswer": true, "prompt": "<p>What is the value of $f(\\var{Input1})$? [[0]]</p>\n<p>What is the value of $f(\\var{Input2})$? [[1]]</p>", "variableReplacementStrategy": "originalfirst", "customMarkingAlgorithm": "", "sortAnswers": false, "type": "gapfill", "scripts": {}, "marks": 0, "unitTests": [], "gaps": [{"showCorrectAnswer": true, "expectedVariableNames": [], "showPreview": true, "variableReplacementStrategy": "originalfirst", "customMarkingAlgorithm": "", "type": "jme", "checkingAccuracy": 0.001, "answer": "{Answer1}", "checkVariableNames": false, "failureRate": 1, "scripts": {}, "marks": 1, "vsetRange": [0, 1], "unitTests": [], "vsetRangePoints": 5, "checkingType": "absdiff", "extendBaseMarkingAlgorithm": true, "variableReplacements": [], "showFeedbackIcon": true}, {"showCorrectAnswer": true, "expectedVariableNames": [], "showPreview": true, "variableReplacementStrategy": "originalfirst", "customMarkingAlgorithm": "", "type": "jme", "checkingAccuracy": 0.001, "answer": "{Answer2}", "checkVariableNames": false, "failureRate": 1, "scripts": {}, "marks": 1, "vsetRange": [0, 1], "unitTests": [], "vsetRangePoints": 5, "checkingType": "absdiff", "extendBaseMarkingAlgorithm": true, "variableReplacements": [], "showFeedbackIcon": true}], "extendBaseMarkingAlgorithm": true, "variableReplacements": [], "showFeedbackIcon": true}], "name": "Joshua's copy of Domain of a piecewise function", "rulesets": {}, "functions": {}, "preamble": {"js": "", "css": ""}, "variables": {"b2": {"definition": "b1+3", "group": "Ungrouped variables", "templateType": "anything", "description": "", "name": "b2"}, "Answer1": {"definition": "{a}*{Input1}+{b}", "group": "Ungrouped variables", "templateType": "anything", "description": "", "name": "Answer1"}, "c": {"definition": "random(-2..2 except 0)", "group": "Ungrouped variables", "templateType": "anything", "description": "", "name": "c"}, "a": {"definition": "random(2..5)", "group": "Ungrouped variables", "templateType": "anything", "description": "", "name": "a"}, "b1": {"definition": "b0+2", "group": "Ungrouped variables", "templateType": "anything", "description": "", "name": "b1"}, "Input1": {"definition": "b0+1", "group": "Ungrouped variables", "templateType": "anything", "description": "", "name": "Input1"}, "Input2": {"definition": "{b2}+4", "group": "Ungrouped variables", "templateType": "anything", "description": "", "name": "Input2"}, "d": {"definition": "random(2..8)", "group": "Ungrouped variables", "templateType": "anything", "description": "", "name": "d"}, "b0": {"definition": "random(1..3)", "group": "Ungrouped variables", "templateType": "anything", "description": "", "name": "b0"}, "b": {"definition": "random(1..3)", "group": "Ungrouped variables", "templateType": "anything", "description": "", "name": "b"}, "Answer2": {"definition": "{c}*({b2}+4)^2+{d}", "group": "Ungrouped variables", "templateType": "anything", "description": "", "name": "Answer2"}}, "advice": "<p>The function $\\simplify{{out}}$ is a piecewise function. It is defined on different parts (or pieces) of its domain by different (sub)functions.</p>\n<p></p>\n<p>In particular, the pieces of the domain are the intervals</p>\n<ul>\n<li>$\\simplify{{inp}}&lt; \\var{b0}$</li>\n<li>$\\var{b0}\\leq \\simplify{{inp}}\\leq&nbsp;\\var{b1}$,</li>\n<li>$\\var{b2}\\leq\\simplify{{inp}}&lt; \\var{b3}$,</li>\n<li>$\\var{b3}&lt;\\simplify{{inp}}\\leq \\var{b4}$ and</li>\n<li>$\\simplify{{inp}}\\ge\\var{b5}$.</li>\n</ul>\n<p>and their corresponding (sub)functions are given by the expressions</p>\n<ul>\n<li>$\\simplify{{p0}}$</li>\n<li>$\\simplify{{p1}}$</li>\n<li>$\\simplify{{p2}}$</li>\n<li>$\\simplify{{p3}}$</li>\n<li>$\\simplify{{p4}}$</li>\n</ul>\n<p></p>\n<p>In the case of the function $\\simplify{{out}}$ above, each of the (sub)functions are defined for the indicated intervals and so the domain of $\\simplify{{out}}$ are all of those intervals combined. The first and second interval join nicely without a gap&nbsp;unlike the rest and so we have \\[\\text{dom}(\\simplify{{out}})=\\{\\simplify{{inp}}\\in\\mathbb{R}:\\, \\simplify{{inp}}\\leq \\var{b1},\\; \\var{b2}\\leq \\simplify{{inp}}&lt;\\var{b3},\\; \\var{b3}&lt;\\simplify{{inp}}\\leq\\var{b4}, \\text{ or }\\; \\simplify{{inp}}\\ge \\var{b5}\\}.\\]</p>\n<p></p>", "type": "question", "contributors": [{"name": "Ben Brawn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/605/"}, {"name": "Joshua Calcutt", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3267/"}]}]}], "contributors": [{"name": "Ben Brawn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/605/"}, {"name": "Joshua Calcutt", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3267/"}]}