// Numbas version: finer_feedback_settings
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This always works, but it is usually quicker if you know the standard patterns.</p>\n<p></p>\n<p>a) See lecture notes and/or panapto video for Lecture 21.2 for the standard shapes of quadratics, cubics, exponentials and $\\ln$ graphs.</p>\n<p></p>\n<p>b)&nbsp;See lecture notes and/or panapto video for Lecture 21.2 for examples of $\\ln$ graphs. Alternatively, see Lecture 21.3 for horizontal translations.</p>\n<p></p>\n<p>c)&nbsp;See lecture notes and/or panapto video for Lecture 21.2 for variations&nbsp;of $\\frac{1}{x}$ graphs. &nbsp;Alternatively, see Lecture 21.3 for horizontal and vertical translations.</p>\n<p></p>\n<p>d) This involves vertical stretching and vertical translations, so see Lecture 21.3.</p>\n<p></p>\n<p>e) This involves a mixture of transformations, so see Lecture 21.3.</p>\n<p></p>\n<p>Again, remember that plugging in $x$-value into the equations is always something you should try doing if all else fails.</p>\n<p></p>", "variablesTest": {"condition": "", "maxRuns": 100}, "functions": {"plotgraph": {"parameters": [["q", "number"], ["a", "number"], ["b", "number"], ["c", "number"]], "definition": "// This functions plots a graph. 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}\n    var f2 = function(x) {return Math.log(x+b);}\n    var f3 = function(x) {return Math.log(x+c);}\n        break;\n    \n    case 3:\n    var f1 = function(x) {return 1/x;}\n    var f2 = function(x) {return 1/x + b;}\n    var f3 = function(x) {return 1/(x-c) -1;}\n        break;\n    \n    case 4:\n    var f1 = function(x) {return Math.sin(x)+a;}\n    var f2 = function(x) {return b*Math.sin(x);}\n    var f3 = function(x) {return c*Math.sin(x) + 2;}\n        break;\n    \n    case 5:\n    var f1 = function(x) {return Math.pow(2.71,x)*-1;}\n    var f2 = function(x) {return Math.pow(2.71,x) - b;}\n    var f3 = function(x) {return Math.pow(2.71,(x-c));}\n    break;\n}\n\n    brd.create('functiongraph', [f1], {strokeWidth:3,strokeColor:'red'});\n    brd.create('functiongraph', [f2], {strokeWidth:3,strokeColor: 'green'});\n    brd.create('functiongraph', [f3], {strokeWidth:3,strokeColor: 'blue'});\n\nreturn div;", "language": "javascript", "type": "html"}}, "statement": "<p>Match the graphs with their&nbsp;equations.</p>", "ungrouped_variables": ["b1", "b2", "c1", "c2", "d1", "d2", "d3", "e2", "e3"], "variables": {"d1": {"description": "", "name": "d1", "group": "Ungrouped variables", "definition": "random(4..6)", "templateType": "anything"}, "d3": {"description": "", "name": "d3", "group": "Ungrouped variables", "definition": "random(2..3)", "templateType": "anything"}, "b1": {"description": "", "name": "b1", "group": "Ungrouped variables", "definition": "random(2..3)", "templateType": "anything"}, "c2": {"description": "", "name": "c2", "group": "Ungrouped variables", "definition": "random(1..3)", "templateType": "anything"}, "c1": {"description": "", "name": "c1", "group": "Ungrouped variables", "definition": "random(2..4)", "templateType": "anything"}, "e3": {"description": "", "name": "e3", "group": "Ungrouped variables", "definition": "random(3..5)", "templateType": "anything"}, "d2": {"description": "", "name": "d2", "group": "Ungrouped variables", "definition": "d1+1", "templateType": "anything"}, "b2": {"description": "", "name": "b2", "group": "Ungrouped variables", "definition": "random(-1,1)-b1", "templateType": "anything"}, "e2": {"description": "", "name": "e2", "group": "Ungrouped variables", "definition": "random(2..3)", "templateType": "anything"}}, "preamble": {"js": "", "css": ""}, "parts": [{"showCorrectAnswer": true, "maxMarks": "1", "minAnswers": 0, "type": "m_n_x", "maxAnswers": 0, "variableReplacements": [], "answers": ["<p>Red</p>", "<p>Green</p>", "<p>Blue</p>"], "scripts": {}, "displayType": "checkbox", "prompt": "<p>{plotgraph(1,0,0,0)}</p>\n<p></p>", "variableReplacementStrategy": "originalfirst", "choices": ["<p>$y=e^x$</p>", "<p>$y=x^2$</p>", "<p>$y=x^3$</p>", "<p>$y=\\ln(x)$</p>"], "minMarks": 0, "matrix": [["1/3", "-1/3", "-1/3"], ["-1/3", "1/3", "-1/3"], ["-1/3", "-1/3", "1/3"], ["-1/3", "-1/3", "-1/3"]], "marks": 0, "layout": {"type": "all", "expression": ""}, "shuffleAnswers": false, "shuffleChoices": true, "showFeedbackIcon": true, "warningType": "none"}, {"showCorrectAnswer": true, "maxMarks": "1", "minAnswers": 0, "type": "m_n_x", "maxAnswers": 0, "variableReplacements": [], "answers": ["<p>Red</p>", "<p>Green</p>", "<p>Blue</p>"], "scripts": {}, "displayType": "checkbox", "prompt": "<p>{plotgraph(4,d1,d2,d3)}</p>\n<p></p>", "variableReplacementStrategy": "originalfirst", "choices": ["<p>$y=\\sin(x)+\\var{d1}$</p>", "<p>$y=\\var{d2}\\sin(x)$</p>", "<p>$y=\\var{d3}\\sin(x) + 2$</p>", "<p>$y = \\sin(x) + \\var{d1+1}$</p>", "<p>$y=\\var{d3+1}\\sin(x)+1$</p>"], "minMarks": 0, "matrix": [["1/3", "-1/3", "-1/3"], ["-1/3", "1/3", "-1/3"], ["-1/3", "-1/3", "1/3"], ["-1/3", "-1/3", "-1/3"], ["-1/3", "-1/3", "-1/3"]], "marks": 0, "layout": {"type": "all", "expression": ""}, "shuffleAnswers": false, "shuffleChoices": true, "showFeedbackIcon": true, "warningType": "none"}], "name": "Patrick's copy of Lovkush's copy of Matching graphs with their equation.", "type": "question", "contributors": [{"name": "Patrick Joyce", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1674/"}]}]}], "contributors": [{"name": "Patrick Joyce", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1674/"}]}