// Numbas version: exam_results_page_options
{"name": "Domain of a polynomial", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Domain of a polynomial", "tags": [], "metadata": {"description": "<p>Multiple choice <g class=\"gr_ gr_5 gr-alert gr_gramm gr_inline_cards gr_run_anim Grammar multiReplace\" id=\"5\" data-gr-id=\"5\">question</g>. Given a randomised polynomial select the <g class=\"gr_ gr_4 gr-alert gr_spell gr_inline_cards gr_run_anim ContextualSpelling ins-del multiReplace gr-progress sel\" id=\"4\" data-gr-id=\"4\">possibe</g> ways of writing the domain of the function.</p>", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "<p>Given the real function below, you should be able to determine its&nbsp;domain.&nbsp;</p>", "advice": "<p>The function {poly} is a polynomial. Regardless of the value of $\\simplify{{inp}}$, the function $\\simplify{{out}}$ will output a number. That is, the domain of $\\simplify{{out}}$ is the set of all real numbers. We can write this as&nbsp;</p>\n<p>\\[\\text{dom}(\\simplify{{out}})=\\mathbb{R}\\]</p>\n<p>or as the open interval</p>\n<p>\\[\\text{dom}(\\simplify{{out}})=(-\\infty,\\infty).\\]</p>\n<p></p>", "rulesets": {}, "extensions": [], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"a": {"name": "a", "group": "Ungrouped variables", "definition": "random(-12..2)", "description": "", "templateType": "anything", "can_override": false}, "c": {"name": "c", "group": "Ungrouped variables", "definition": "[random(-12..12 except 0)]+repeat(random(0,random(-12..12 except 0)),n-1)+[random(-12..12 except 0)]", "description": "", "templateType": "anything", "can_override": false}, "n": {"name": "n", "group": "Ungrouped variables", "definition": "random(1..5)", "description": "", "templateType": "anything", "can_override": false}, "poly": {"name": "poly", "group": "Ungrouped variables", "definition": "if(n=2,'\\$\\\\var{out}\\\\left(\\\\var{inp}\\\\right)=\\\\simplify{{c[0]}+{c[1]}{inp}+{c[2]}{inp}^2}\\$',\nif(n=3, '\\$\\\\var{out}\\\\left(\\\\var{inp}\\\\right)=\\\\simplify{{c[0]}+{c[1]}{inp}+{c[2]}{inp}^2+{c[3]}{inp}^3}\\$',\nif(n=4, '\\$\\\\var{out}\\\\left(\\\\var{inp}\\\\right)=\\\\simplify{{c[0]}+{c[1]}{inp}+{c[2]}{inp}^2+{c[3]}{inp}^3+{c[4]}{inp}^4}\\$',\nif(n=5, '\\$\\\\var{out}\\\\left(\\\\var{inp}\\\\right)=\\\\simplify{{c[0]}+{c[1]}{inp}+{c[2]}{inp}^2+{c[3]}{inp}^3+{c[4]}{inp}^4+{c[5]}{inp}^5}\\$',\n        '\\$\\\\var{out}\\\\left(\\\\var{inp}\\\\right)=\\\\simplify{{c[0]}+{c[1]}{inp}}\\$'))))", "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}, "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..10)", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["out", "inp", "n", "c", "poly", "a", "b"], "variable_groups": [], "functions": {}, "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": "<p>Which of the following represents the domain of {poly}?</p>\n<p></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>$(-\\infty,\\infty)$</p>", "<p>$\\{\\simplify{{inp}}\\in\\mathbb{R}:\\, \\var{a}\\leq\\simplify{{inp}}\\leq\\var{b}\\}$</p>", "<p>$\\{\\simplify{{inp}}\\in\\mathbb{R}:\\, \\var{a}&lt;\\simplify{{inp}}&lt;\\var{b}\\}$</p>", "<p>$\\{\\simplify{{inp}}\\in\\mathbb{R}:\\, \\simplify{{inp}}\\ne \\var{c[0]}\\}$</p>", "<p>$\\{\\simplify{{inp}}\\in\\mathbb{R}:\\, \\simplify{{inp}}&lt;\\var{a}\\, \\text{or} \\,\\simplify{{inp}}\\ge\\var{b}\\}$</p>"], "matrix": ["1", "1", 0, 0, 0, 0], "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/"}]}]}], "contributors": [{"name": "Ben Brawn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/605/"}]}