// Numbas version: exam_results_page_options
{"name": "Interaction: enter domain with brackets", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Interaction: enter domain with brackets", "tags": [], "metadata": {"description": "", "licence": "None specified"}, "statement": "<p>Find the domain of the function $f(x)=\\sqrt{\\frac{\\var{a}-x}{x+\\var{b}}}$.</p>", "advice": "<p>A square root is only defined for positive values, so we need to solve the inequality $g(x)=\\frac{\\var{a}-x}{x+\\var{b}}\\geq 0$.&nbsp; &nbsp;We make a sign chart for the rational function $g$</p>\n<ol>\n<li>domain is all real numbers except $\\var{-b}$;</li>\n<li>there is one zero at $\\var{a}$;</li>\n<li>there are 3 regions to consider: $x&lt;\\var{-b}$, $\\var{-b}&lt;x&lt;\\var{a}$ and $\\var{a}&lt;x$.&nbsp; By evaluating the rational function at any point of a given region, we establish that it takes negative values on the first and the third region and positive values on the second.</li>\n</ol>\n<p>This results in the following sign chart:</p>\n<table style=\"border-style: inset; margin-left: auto; margin-right: auto;\" border=\"Y\">\n<tbody>\n<tr>\n<td style=\"text-align: center;\">$x$</td>\n<td style=\"text-align: center;\"></td>\n<td style=\"text-align: center;\">$\\var{-b}$</td>\n<td style=\"text-align: center;\"></td>\n<td style=\"text-align: center;\">$\\var{a}$</td>\n<td style=\"text-align: center;\"></td>\n</tr>\n<tr>\n<td style=\"text-align: center;\">$g(x)$</td>\n<td style=\"text-align: center;\">$-$</td>\n<td style=\"text-align: center;\">\\</td>\n<td style=\"text-align: center;\">$+$</td>\n<td style=\"text-align: center;\">0</td>\n<td style=\"text-align: center;\">$-$</td>\n</tr>\n</tbody>\n</table>\n<p>So, the domain is given by $]\\var{-b},\\var{a}]$.</p>", "rulesets": {}, "extensions": [], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"a": {"name": "a", "group": "Ungrouped variables", "definition": "random(1..15)", "description": "", "templateType": "anything", "can_override": false}, "b": {"name": "b", "group": "Ungrouped variables", "definition": "random(1..15)", "description": "", "templateType": "anything", "can_override": false}, "end_point": {"name": "end_point", "group": "Ungrouped variables", "definition": "(a-1)/b", "description": "", "templateType": "anything", "can_override": false}, "pos_point": {"name": "pos_point", "group": "Ungrouped variables", "definition": "a/b", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["a", "b", "end_point", "pos_point"], "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>The domain of this function is a single interval, namely: [[0]][[1]],[[2]][[3]].&nbsp;</p>\n<p><strong>Instructions on entering your answer:</strong></p>\n<p>You will need to fill out 4 parts of an interval:&nbsp;</p>\n<ul>\n<li>bracket on the left: pick the correct one from the drop-down menu: <strong>[</strong> means 'include the value that follows'; <strong>]</strong> means 'exclude the value that follows' ;&nbsp;</li>\n<li>bounding value on the left of the interval: this is either a real number or $-\\infty$, which you enter as <strong>- infinity</strong> ;</li>\n<li>bounding value on the right of the interval: this is either a real number or $+\\infty$, which you enter as <strong>+ infinity</strong> ;</li>\n<li>bracket on the right: pick the correct one from the drop-down menu: <strong>[</strong> means 'exclude the value that preceeds'; <strong>]</strong> means 'include the value that preceeds'.</li>\n</ul>\n<p>Do not round values, enter a fraction if necessary.</p>", "gaps": [{"type": "1_n_2", "useCustomName": true, "customName": "left_bracket", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minMarks": 0, "maxMarks": 0, "shuffleChoices": false, "displayType": "dropdownlist", "displayColumns": 0, "showCellAnswerState": true, "choices": ["[", "]"], "matrix": [0, "0.025"], "distractors": ["", ""]}, {"type": "jme", "useCustomName": true, "customName": "left_bound", "marks": "0.1", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "{-b}", "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": []}, {"type": "jme", "useCustomName": true, "customName": "right_bound", "marks": "0.1", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "{a}", "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": []}, {"type": "1_n_2", "useCustomName": true, "customName": "right_bracket", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minMarks": 0, "maxMarks": 0, "shuffleChoices": false, "displayType": "dropdownlist", "displayColumns": 0, "showCellAnswerState": true, "choices": ["[", "]"], "matrix": [0, "0.025"], "distractors": ["", ""]}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "contributors": [{"name": "Eric Boeckx", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3901/"}, {"name": "Ilse Spruyt", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4163/"}, {"name": "Alexander Holvoet", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/19859/"}]}]}], "contributors": [{"name": "Eric Boeckx", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3901/"}, {"name": "Ilse Spruyt", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4163/"}, {"name": "Alexander Holvoet", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/19859/"}]}