// Numbas version: finer_feedback_settings
{"name": "Identify the hyperbolic function from its graph", "extensions": [], "custom_part_types": [], "resources": [["question-resources/sinh_sketch.png", "sinh_sketch.png"], ["question-resources/cosh_sketch.png", "cosh_sketch.png"], ["question-resources/tanh_sketch.png", "tanh_sketch.png"]], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Identify the hyperbolic function from its graph", "tags": [], "metadata": {"description": "<p>Multiple choice of hyperbolic functions (image of graph given).</p>", "licence": "Creative Commons Attribution-NonCommercial 4.0 International"}, "statement": "<p>Which hyperbolic function is represented by this graph?</p>", "advice": "<p>This is a graph of</p>\n<p><span data-jme-visible=\"Ans=&quot;y=sinh(x)&quot;\">$y=\\sinh(x)=\\frac{e^{x}-e^{-x}}{2}$</span></p>\n<p><span data-jme-visible=\"Ans=&quot;y=sinh(x)&quot;\">Notice that at $x$ increases, $\\sinh(x)$ looks like an exponential curve.&nbsp; This is because it approximates $\\frac{e^x}{2}$ as the $e^{-x}$ term becomes negligible.</span></p>\n<p><span data-jme-visible=\"Ans=&quot;y=sinh(x)&quot;\">Similarly, as $x$ decreases, the graph looks likle the curve $-\\frac{e^{-x}}{2}$.</span><span data-jme-visible=\"Ans=&quot;y=sinh(x)&quot;\">&nbsp;</span></p>\n<p><span data-jme-visible=\"Ans=&quot;y=cosh(x)&quot;\">$y=\\cosh(x)=\\frac{e^{x}+e^{-x}}{2}$</span></p>\n<div data-jme-visible=\"Ans=&quot;y=cosh(x)&quot;\">\n<p>Notice that at $x$ increases, $\\cosh(x)$ looks like an exponential curve.&nbsp; This is because it approximates $\\frac{e^x}{2}$ as the $e^{-x}$ term becomes negligible.</p>\n</div>\n<p><span data-jme-visible=\"Ans=&quot;y=cosh(x)&quot;\">Similarly, as $x$ decreases, the graph looks like the curve $\\frac{e^{-x}}{2}$.</span></p>\n<p><span data-jme-visible=\"Ans=&quot;y=cosh(x)&quot;\">You may recall that this curve can be though of as an average of the functions $\\frac{e^x}{2}$ and $\\frac{e^{-x}}{2}$&nbsp;</span></p>\n<p><span data-jme-visible=\"Ans=&quot;y=tanh(x)&quot;\">$y=\\tanh(x)=\\frac{\\sinh(x)}{\\cosh(x)}=\\frac{e^{2x}-1}{e^{2x}+1}$</span><span data-jme-visible=\"Ans=&quot;y=tanh(x)&quot;\"></span></p>\n<p><span data-jme-visible=\"Ans=&quot;y=tanh(x)&quot;\">Notice that at $x$ increases in the positive direction, $\\tanh(x)$ tends to 1.&nbsp; Similarly, as $x$ increases in the negative directions, $\\tanh(x) \\rightarrow -1$.</span></p>\n<p>You may wish to look back at the graphs chapter of this resource for a more thorough explanation.</p>", "rulesets": {}, "extensions": [], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true, "j": false}, "constants": [], "variables": {"functions": {"name": "functions", "group": "Ungrouped variables", "definition": "shuffle([\"y=cosh(x)\",\"y=sinh(x)\",\"y=tanh(x)\"])", "description": "", "templateType": "anything", "can_override": false}, "Ans": {"name": "Ans", "group": "Ungrouped variables", "definition": "functions[0]", "description": "", "templateType": "anything", "can_override": false}, "wrong1": {"name": "wrong1", "group": "Ungrouped variables", "definition": "functions[1]", "description": "", "templateType": "anything", "can_override": false}, "wrong2": {"name": "wrong2", "group": "Ungrouped variables", "definition": "functions[2]", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["functions", "Ans", "wrong1", "wrong2"], "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><span data-jme-visible=\"Ans=&quot;y=sinh(x)&quot;\"><img src=\"resources/question-resources/sinh_sketch.png\"/></span></p>\n<p><span data-jme-visible=\"Ans=&quot;y=cosh(x)&quot;\"><img src=\"resources/question-resources/cosh_sketch.png\"/></span></p>\n<p></p>\n<p><span data-jme-visible=\"Ans=&quot;y=tanh(x)&quot;\"><img src=\"resources/question-resources/tanh_sketch.png\"/></span></p>", "minMarks": 0, "maxMarks": 0, "shuffleChoices": true, "displayType": "radiogroup", "displayColumns": 0, "showBlankOption": true, "showCellAnswerState": true, "choices": ["{Ans}", "{wrong1}", "{wrong2}"], "matrix": ["1", 0, 0], "distractors": ["", "", ""]}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "contributors": [{"name": "Will Roberts", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/32402/"}], "resources": ["question-resources/sinh_sketch.png", "question-resources/cosh_sketch.png", "question-resources/tanh_sketch.png"]}]}], "contributors": [{"name": "Will Roberts", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/32402/"}]}