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{"name": "Algebra: graphs of functions, straight line [L2 Randomised]", "extensions": ["jsxgraph"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"variablesTest": {"condition": "", "maxRuns": 100}, "variables": {"x": {"definition": "vector(shuffle(-4..4 except (0)))", "name": "x", "description": "", "templateType": "anything", "group": "part a"}, "cf": {"definition": "random(-5..5)", "name": "cf", "description": "", "templateType": "anything", "group": "part a"}, "fx": {"definition": "x*mf+vector(cf,cf,cf,cf,cf,cf,cf,cf)", "name": "fx", "description": "", "templateType": "anything", "group": "part a"}, "mf": {"definition": "random(-4..4 except 0)", "name": "mf", "description": "", "templateType": "anything", "group": "part a"}}, "preamble": {"css": "", "js": ""}, "extensions": ["jsxgraph"], "rulesets": {}, "variable_groups": [{"name": "part a", "variables": ["mf", "cf", "x", "fx"]}], "parts": [{"showCorrectAnswer": true, "type": "gapfill", "marks": 0, "gaps": [{"maxValue": "fx[0]", "showCorrectAnswer": true, "correctAnswerStyle": "plain", "allowFractions": false, "mustBeReducedPC": 0, "type": "numberentry", "marks": "1", "extendBaseMarkingAlgorithm": true, "variableReplacements": [], "customMarkingAlgorithm": "", "showFeedbackIcon": true, "scripts": {}, "minValue": "fx[0]", "notationStyles": ["plain", "en", "si-en"], "mustBeReduced": false, "correctAnswerFraction": false, "variableReplacementStrategy": "originalfirst", "unitTests": []}, {"maxValue": "fx[1]", "showCorrectAnswer": true, "correctAnswerStyle": "plain", "allowFractions": false, "mustBeReducedPC": 0, "type": "numberentry", "marks": "1", "extendBaseMarkingAlgorithm": true, "variableReplacements": [], "customMarkingAlgorithm": "", "showFeedbackIcon": true, "scripts": {}, "minValue": "fx[1]", "notationStyles": ["plain", "en", "si-en"], "mustBeReduced": false, "correctAnswerFraction": false, "variableReplacementStrategy": "originalfirst", "unitTests": []}, {"maxValue": "x[2]", "showCorrectAnswer": true, "correctAnswerStyle": "plain", "allowFractions": false, "mustBeReducedPC": 0, "type": "numberentry", "marks": "1", "extendBaseMarkingAlgorithm": true, "variableReplacements": [], "customMarkingAlgorithm": "", "showFeedbackIcon": true, "scripts": {}, "minValue": "x[2]", "notationStyles": ["plain", "en", "si-en"], "mustBeReduced": false, "correctAnswerFraction": false, "variableReplacementStrategy": "originalfirst", "unitTests": []}, {"maxValue": "x[3]", "showCorrectAnswer": true, "correctAnswerStyle": "plain", "allowFractions": false, "mustBeReducedPC": 0, "type": "numberentry", "marks": "1", "extendBaseMarkingAlgorithm": true, "variableReplacements": [], "customMarkingAlgorithm": "", "showFeedbackIcon": true, "scripts": {}, "minValue": "x[3]", "notationStyles": ["plain", "en", "si-en"], "mustBeReduced": false, "correctAnswerFraction": false, "variableReplacementStrategy": "originalfirst", "unitTests": []}, {"maxValue": "x[4]", "showCorrectAnswer": true, "correctAnswerStyle": "plain", "allowFractions": false, "mustBeReducedPC": 0, "type": "numberentry", "marks": "1", "extendBaseMarkingAlgorithm": true, "variableReplacements": [], "customMarkingAlgorithm": "", "showFeedbackIcon": true, "scripts": {}, "minValue": "x[4]", "notationStyles": ["plain", "en", "si-en"], "mustBeReduced": false, "correctAnswerFraction": false, "variableReplacementStrategy": "originalfirst", "unitTests": []}, {"checkVariableNames": false, "showCorrectAnswer": true, "expectedVariableNames": [], "vsetRangePoints": 5, "checkingType": "absdiff", "type": "jme", "showPreview": true, "marks": "2", "vsetRange": [0, 1], "extendBaseMarkingAlgorithm": true, "variableReplacements": [], "customMarkingAlgorithm": "", "showFeedbackIcon": true, "scripts": {}, "failureRate": 1, "checkingAccuracy": 0.001, "answer": "{mf}x+{cf}", "variableReplacementStrategy": "originalfirst", "unitTests": []}, {"maxValue": "x[2]", "showCorrectAnswer": true, "correctAnswerStyle": "plain", "allowFractions": false, "mustBeReducedPC": 0, "type": "numberentry", "marks": "1", "extendBaseMarkingAlgorithm": true, "variableReplacements": [], "customMarkingAlgorithm": "", "showFeedbackIcon": true, "scripts": {}, "minValue": "x[2]", "notationStyles": ["plain", "en", "si-en"], "mustBeReduced": false, "correctAnswerFraction": false, "variableReplacementStrategy": "originalfirst", "unitTests": []}], "extendBaseMarkingAlgorithm": true, "variableReplacements": [], "customMarkingAlgorithm": "", "showFeedbackIcon": true, "scripts": {}, "prompt": "<p>This is the graph of a function $f$.</p>\n<p>{eqnline(mf, cf)}</p>\n<p></p>\n<p>(i) $f(\\var{x[0]}) =$ [[0]]</p>\n<p>(ii) $f(\\var{x[1]}) =$ [[1]]</p>\n<p>(iii) What value for&nbsp;$a$ do you need so that $f(a) = \\var{fx[2]}$? [[2]]</p>\n<p>(iv) What is $f^{-1}(\\var{fx[3]})$? [[3]]</p>\n<p>(v) Solve the equation $f(x) = \\var{fx[4]}$. &nbsp; &nbsp;$x=$[[4]]</p>\n<p>(vi) What is the equation of the line? &nbsp;$y=$ [[5]]</p>\n<p>(vii) $f^{-1}(\\var{fx[2]})=$ [[6]]</p>", "sortAnswers": false, "variableReplacementStrategy": "originalfirst", "unitTests": []}], "tags": ["l2", "L2"], "advice": "<p></p>\n<ul>\n<li>Remember to check your answers. &nbsp;For example, to check your answer for (vi), you should plug-in values for $x$, calculate the value of $y$, and check the coordinates. &nbsp;For example, if I plug $x=1$ into the equation, I get $y= \\var{mf} \\times 1 + \\var{cf} = \\var{mf+cf}$. &nbsp;I then check whether the coordinate $(1, \\var{mf+cf})$ lies on the graph or not; in this instance it does, so that is a good sign. It is worth checking one or two other coordinates to really make sure.</li>\n</ul>\n<p></p>\n<ul>\n<li>You should notice that (iii), (iv) and (v) are asking the same question, but in different guises. &nbsp;If you do not understand this, then <g class=\"gr_ gr_15 gr-alert gr_spell gr_inline_cards gr_run_anim ContextualSpelling ins-del\" id=\"15\" data-gr-id=\"15\">re-view</g> the lectures. If that does not help, then please ask us and we will help.</li>\n</ul>\n<p></p>\n<p></p>", "metadata": {"description": "<p><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;A graph of a straight line $f$ is given. Questions include determining values of $f$, of $f$ inverse, and determing the equation of the line. Non-calculator. Detail advice is given.&quot;}\" data-sheets-userformat=\"{&quot;2&quot;:513,&quot;3&quot;:[null,0],&quot;12&quot;:0}\">A graph of a straight line $f$ is given. Questions include determining values of $f$, of <g class=\"gr_ gr_5 gr-alert gr_tiny gr_gramm gr_inline_cards gr_run_anim Grammar only-ins doubleReplace replaceWithoutSep\" id=\"5\" data-gr-id=\"5\">$</g>f$ inverse, and determining the equation of the line.</span></p>", "licence": "Creative Commons Attribution 4.0 International"}, "ungrouped_variables": [], "statement": "<p>This is a non-calculator question.</p>", "name": "Algebra: graphs of functions, straight line [L2 Randomised]", "functions": {"eqnline": {"language": "javascript", "definition": "// This functions plots a cubic with a certain number of\n// stationary points and roots.\n// It creates the board, sets it up, then returns an\n// HTML div tag containing the board.\n\n\n// Max and min x and y values for the axis.\nvar x_min = -6;\nvar x_max = 6;\nvar y_min = -20;\nvar y_max = 20;\n\n\n// First, make the JSXGraph board.\nvar div = Numbas.extensions.jsxgraph.makeBoard(\n  '500px',\n  '600px',\n {\n   boundingBox: [x_min,y_max,x_max,y_min],\n   axis: false,\n   showNavigation: true,\n   grid: true\n }\n);\n\n\n\n\n// div.board is the object created by JSXGraph, which you use to \n// manipulate elements\nvar board = div.board; \n\n// create the x-axis and y-axis\nvar xaxis = board.create('axis',[[0,0],[1,0]]);\n\n// create the y-axis\nvar yaxis = board.create('axis',[[0,0],[0,1]], );\n\n\n\n\n// Plot the function.\n    board.create('functiongraph',\n             [function(x){ return m*x+c},x_min,x_max]);\n\n\n\nreturn div;", "type": "html", "parameters": [["m", "number"], ["c", "number"]]}}, "type": "question", "contributors": [{"name": "Lovkush Agarwal", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1358/"}, {"name": "Abbi Mullins", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2466/"}, {"name": "Matthew James Sykes", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2582/"}]}]}], "contributors": [{"name": "Lovkush Agarwal", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1358/"}, {"name": "Abbi Mullins", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2466/"}, {"name": "Matthew James Sykes", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2582/"}]}