// Numbas version: finer_feedback_settings
{"name": "Domain of an exponential", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Domain of an exponential", "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\" 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 functions below, you should be able to determine their domains.&nbsp;</p>", "advice": "<p>a) The function $f(x)=e^x$ is an exponential function. Regardless of the value of $x$, the function $f$ will output a number. That is, the domain of $f$ is the set of all real numbers. We can write this as&nbsp;</p>\n<p>\\[\\text{dom}(f)=\\mathbb{R}\\]</p>\n<p>or as the open interval</p>\n<p>\\[\\text{dom}(f)=(-\\infty,\\infty).\\]</p>\n<p></p>\n<p>b) The function $ \\var{out}(\\var{inp}) =\\simplify{ {c[0]}*{b}^({c[2]}{inp}+{c[3]})+{c[4]}} $ is also an exponential function. 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>", "rulesets": {}, "extensions": [], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"inp": {"name": "inp", "group": "Ungrouped variables", "definition": "expression(random('x','r','s','t','w'))", "description": "", "templateType": "anything", "can_override": false}, "c": {"name": "c", "group": "Ungrouped variables", "definition": "shuffle(-12..12 except [-1,0,1])[0..5]", "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": "random(2..12)", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["out", "inp", "c", "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 $f(x)=e^x$?</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>$\\{x\\in\\mathbb{R}:\\, x&gt;0\\}$</p>", "<p>$\\{x\\in\\mathbb{R}:\\, x\\ge 0\\}$</p>", "<p>$\\{x\\in\\mathbb{R}:\\, -e&lt;x&lt; e\\}$</p>", "<p>$\\{x\\in\\mathbb{R}:\\, x\\ne 0\\}$</p>"], "matrix": ["1", "1", 0, 0, 0, 0], "distractors": ["", "", "", "", "", ""]}, {"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 $ \\var{out}(\\var{inp}) =\\simplify{ {c[0]}*{b}^({c[2]}{inp}+{c[3]})+{c[4]}} $?</p>", "minMarks": 0, "maxMarks": 0, "shuffleChoices": true, "displayType": "checkbox", "displayColumns": "1", "minAnswers": 0, "maxAnswers": 0, "warningType": "none", "showCellAnswerState": true, "markingMethod": "sum ticked cells", "choices": ["<p>$\\mathbb{R}$</p>", "<p>$(-\\infty,\\infty)$</p>", "<p>$\\{\\simplify{{inp}}\\in\\mathbb{R}:\\, \\simplify{{inp}}\\ge \\var{c[4]}\\}$</p>", "<p>$\\{\\simplify{{inp}}\\in\\mathbb{R}:\\, \\simplify{{inp}}&gt;0\\}$</p>", "<p>$\\{\\simplify{{inp}}\\in\\mathbb{R}:\\, \\simplify{{inp}}\\ne \\simplify{-{c[3]}/{c[2]}}\\}$</p>", "<p>$\\{\\simplify{{inp}}\\in\\mathbb{R}:\\, \\simplify{{inp}}&lt;\\var{-b}\\, \\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", "type": "question", "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/"}]}