// Numbas version: exam_results_page_options
{"name": "Rational functions 2", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Rational functions 2", "tags": [], "metadata": {"description": "Evaluating y intercept and horizontal and vertical asymptote for a rational function.&nbsp;", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "<p>Let $f(x) = \\frac{ \\var{a}&nbsp;x + \\var{b}}{ \\var{c} x- \\var{d} }, x \\ne \\frac { \\var{-d} }{ \\var{c}} $.</p>", "advice": "<p>In part (a) the vertical asymptote can be found by noting where x is undefined (the value of x which makes the denominator zero. $x = - \\frac{ \\var{d} }{ \\var{c} }$.</p>\n<p>In part (b) the y-intercept corresponds to the function evaluated when $x = 0$. The y-coordinate is given by $\\var{b} \\div \\var{-d}$.</p>\n<p>y-intercept is $(0, -\\frac {\\var{b}}{\\var{d}})$</p>\n<p>In part (c) the horizontal asymptote is the behaviour of the function as $x&nbsp; \\to \\infty$ which approaches&nbsp;$&nbsp;\\frac{ \\var{a} }{ \\var{c} }$</p>\n<p>horizontal asymptote is, therefore, $y = 3$.</p>\n<p></p>", "rulesets": {}, "extensions": [], "variables": {"a": {"name": "a", "group": "Ungrouped variables", "definition": "3*c", "description": "<p>a in function (ax - b)/(cx + d)</p>", "templateType": "anything"}, "c_list": {"name": "c_list", "group": "Ungrouped variables", "definition": "[ 2, 2, 3, 3, 3, 4, 4 ]", "description": "", "templateType": "list of numbers"}, "b": {"name": "b", "group": "Ungrouped variables", "definition": "random(1 .. 4#1)", "description": "<p>b&nbsp;in function (ax - b)/(cx + d)</p>", "templateType": "randrange"}, "d_list": {"name": "d_list", "group": "Ungrouped variables", "definition": "[ 1, 3, 1, 2, 4, 1, 3 ]", "description": "<p>d&nbsp;in function (ax - b)/(cx + d)</p>", "templateType": "list of numbers"}, "randomise_question": {"name": "randomise_question", "group": "Ungrouped variables", "definition": "random(0 .. 6#1)", "description": "", "templateType": "randrange"}, "c": {"name": "c", "group": "Ungrouped variables", "definition": "c_list[randomise_question]", "description": "", "templateType": "anything"}, "d": {"name": "d", "group": "Ungrouped variables", "definition": "d_list[randomise_question]", "description": "", "templateType": "anything"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["a", "c_list", "b", "d_list", "randomise_question", "c", "d"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "patternmatch", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Write down the equation of the vertical asymptote.</p>", "answer": "x[ ]*=[ ]*-[ ]*{d}[ ]*/[ ]*{c}", "displayAnswer": "x=-{d}/{c}", "matchMode": "regex"}, {"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>Write down the coordinates of the y-intercept.</p>\n<p>([[0]].[[1]])</p>", "gaps": [{"type": "numberentry", "useCustomName": true, "customName": "xcoord", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": false, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "0", "maxValue": "0", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en", "eu", "plain-eu"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": true, "customName": "ycoord", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": false, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "{-b}/{d}", "maxValue": "{-b}/{d}", "correctAnswerFraction": true, "allowFractions": true, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en", "eu", "plain-eu"], "correctAnswerStyle": "plain"}], "sortAnswers": false}, {"type": "patternmatch", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Write the equation of the horizontal asymptote.</p>", "answer": "y[ ]*=[ ]*3", "displayAnswer": "y=3", "matchMode": "regex"}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "contributors": [{"name": "Johnathan Gregg", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4974/"}]}]}], "contributors": [{"name": "Johnathan Gregg", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4974/"}]}