// Numbas version: finer_feedback_settings
{"name": "Graphs: visualising a non linear graph 1", "extensions": ["geogebra"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Graphs: visualising a non linear graph 1", "tags": [], "metadata": {"description": "<p>Identifying which graph shows the function $y=\\frac{x-a}{x+b}$</p>", "licence": "None specified"}, "statement": "", "advice": "<p>Look for the intersections with the axis, and the behaviour of the graph as $x$ becomes large.<br/><br/>When $x=\\var{a}$, $y=0$, therefore there will be an intersection with the $x-\\text{axis}$ at $(\\var{a},0)$.<br/><br/>When $x=0$, $y=\\frac{0-\\var{a}}{0+\\var{b}}$, therefore there will be an intersection with the $y-\\text{axis}$ at $(0,\\simplify{-{a}/{b}})$.<br/><br/>When $x$ becomes very large, $(x+a) \\rightarrow x$ and $(x-b) \\rightarrow x$, therefore $f(x) \\rightarrow 1$. &nbsp;Therefore there is an asymptote at $x=1$.</p>", "rulesets": {}, "extensions": ["geogebra"], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"a": {"name": "a", "group": "Ungrouped variables", "definition": "random(-5..5)", "description": "", "templateType": "anything", "can_override": false}, "b": {"name": "b", "group": "Ungrouped variables", "definition": "random(-5..3 except a)", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["a", "b"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "1_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 graph shows the&nbsp;function $\\frac{\\simplify{x-{a}}}{\\simplify{x+{b}}}$?</p>", "minMarks": 0, "maxMarks": 0, "shuffleChoices": true, "displayType": "radiogroup", "displayColumns": 0, "showCellAnswerState": true, "choices": ["{geogebra_applet('https://www.geogebra.org/m/rybufkft',[a: b, b: a])}", "{geogebra_applet('https://www.geogebra.org/m/rybufkft',[a: -a, b: b])}", "{geogebra_applet('https://www.geogebra.org/m/rybufkft',[a: a, b: b])}"], "matrix": [0, 0, "1"], "distractors": ["", "", ""]}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "type": "question", "contributors": [{"name": "Ruth Hand", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3228/"}, {"name": "Ben McGovern", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4872/"}]}]}], "contributors": [{"name": "Ruth Hand", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3228/"}, {"name": "Ben McGovern", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4872/"}]}