// Numbas version: finer_feedback_settings
{"name": "Graphing: linear", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Graphing: linear", "tags": ["graphing", "linear", "polynomials", "sketching", "straight lines"], "metadata": {"description": "", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "<p>You are given the equation&nbsp;$y=\\simplify[all,fractionNumbers]{{a}x+{b}}$.&nbsp;</p>", "advice": "", "rulesets": {}, "extensions": [], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true, "j": false}, "constants": [], "variables": {"a": {"name": "a", "group": "Ungrouped variables", "definition": "random(-6..6 except 0)", "description": "", "templateType": "anything", "can_override": false}, "lleading": {"name": "lleading", "group": "Ungrouped variables", "definition": "[if(a<0,1,0),if(a<0,0,1)]", "description": "", "templateType": "anything", "can_override": false}, "b": {"name": "b", "group": "Ungrouped variables", "definition": "random(-10..10)", "description": "", "templateType": "anything", "can_override": false}, "rleading": {"name": "rleading", "group": "Ungrouped variables", "definition": "[if(a>0,1,0),if(a>0,0,1)]", "description": "", "templateType": "anything", "can_override": false}, "xints": {"name": "xints", "group": "Ungrouped variables", "definition": "set(-b/a)", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["a", "b", "lleading", "rleading", "xints"], "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>The equation $y=\\simplify[all,fractionNumbers]{{a}x+{b}}$, or its graph, can be described as a</p>", "stepsPenalty": "1", "steps": [{"type": "information", "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>An equation of the form $y=ax+b$ is&nbsp;known as&nbsp;a linear equation,&nbsp;and its graph is a straight line.&nbsp;</p>"}], "minMarks": 0, "maxMarks": 0, "shuffleChoices": true, "displayType": "radiogroup", "displayColumns": 0, "showCellAnswerState": true, "choices": ["<p>straight line</p>", "<p>parabola/quadratic</p>", "<p>cubic</p>", "<p>hyperbola</p>", "<p>circle</p>", "<p>quartic</p>"], "matrix": ["1", "0", "0", 0, 0, 0], "distractors": ["", "", "", "", "", ""]}, {"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>As we move to the far left of the graph of $y=\\simplify[all,fractionNumbers]{{a}x+{b}}$, the graph</p>", "stepsPenalty": "1", "steps": [{"type": "information", "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>What happens to the graph as you go far to the left or right is called the long term behaviour of a graph.</p>\n<p>The leading term (the term that includes the highest power) determines the long term behaviour of a&nbsp;polynomial. In our polynomial the leading term is&nbsp;$\\simplify[all,fractionNumbers]{{a}x}$.</p>\n<p>As we go far to the left of the graph $x$ is negative, and so $\\simplify[all,fractionNumbers]{{a}x}$&nbsp;<span data-jme-visible=\"a&gt;0\">is negative. That is, the graph goes downwards.</span>&nbsp;<span data-jme-visible=\"a&lt;0\">is positive. That is, the graph goes upwards.</span>&nbsp;</p>\n<p></p>"}], "minMarks": 0, "maxMarks": 0, "shuffleChoices": false, "displayType": "radiogroup", "displayColumns": 0, "showCellAnswerState": true, "choices": ["<p>goes upwards.</p>", "<p>goes downwards.</p>"], "matrix": "lleading"}, {"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>As we move to the far right of the graph of $y=\\simplify[all,fractionNumbers]{{a}x+{b}}$, the graph</p>", "stepsPenalty": "1", "steps": [{"type": "information", "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>What happens to the graph as you go far to the left or right is called the long term behaviour of a graph.</p>\n<p>The leading term (the term that includes the highest power) determines the long term behaviour of a&nbsp;polynomial. In our polynomial the leading term is&nbsp;$\\simplify[all,fractionNumbers]{{a}x}$.</p>\n<p>As we go far to the right&nbsp;of the graph $x$ is positive, and so $\\simplify[all,fractionNumbers]{{a}x}$&nbsp;<span data-jme-visible=\"a&lt;0\">is negative. That is, the graph goes downwards.</span>&nbsp;<span data-jme-visible=\"a&gt;0\">is positive. That is, the graph goes upwards.</span>&nbsp;</p>\n<p></p>"}], "minMarks": 0, "maxMarks": 0, "shuffleChoices": false, "displayType": "radiogroup", "displayColumns": 0, "showCellAnswerState": true, "choices": ["<p>goes upwards.</p>", "<p>goes downwards.</p>"], "matrix": "rleading"}, {"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>The $y$-intercept of the graph of $y=\\simplify[all,fractionNumbers]{{a}x+{b}}$ is $y=$[[0]].</p>", "stepsPenalty": "1", "steps": [{"type": "information", "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>The $y$-intercept is the value of $y$ when $x=0$, that is, the value of $y$ where the graph hits&nbsp;the $y$-axis. To find it, substitute $x=0$ into our equation:</p>\n<p>\\[y=\\simplify[unitFactor,basic,fractionNumbers]{{a}0+{b}}=\\var{b}.\\]</p>\n<p></p>"}], "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "{b}", "maxValue": "{b}", "correctAnswerFraction": true, "allowFractions": true, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": false, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}, {"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>The set of $x$-intercepts of the graph of $y=\\simplify[all,fractionNumbers]{{a}x+{b}}$ would be [[0]].</p>\n<p><strong>Note:&nbsp;</strong>If there are no intercepts, enter<strong> <strong>set()</strong></strong></p>\n<p><span>If there is only one intercept, say $x=5$, enter <strong><strong>set(5)</strong></strong></span></p>\n<p><span>If there are two intercepts, say $x=-2$ and $x=1.5$, enter <strong>set(-2,1.5)</strong></span></p>\n<p><span>If there are three intercepts, say $x=-2$,&nbsp;$x=1.5$ and $x=5$, enter<strong> <strong>set(-2,1.5,5)</strong></strong></span></p>\n<p></p>", "stepsPenalty": "1", "steps": [{"type": "information", "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>The $x$-intercept is the value of $x$ when $y=0$, that is, the value of $x$ where the graph hits&nbsp;the $x$-axis. To find it, substitute $y=0$ into our equation:</p>\n<p>\\[0=\\simplify[all,fractionNumbers]{{a}x+{b}} \\]</p>\n<p></p>\n<p>Solving this&nbsp;equation tells us that&nbsp;the $x$-intercept is $x=\\simplify[all, fractionNumbers]{{-b}/{a}}$.</p>"}], "gaps": [{"type": "jme", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "{xints}", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": []}], "sortAnswers": false}, {"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>Given the degree of a polynomial is $1$, the maximum number of possible 'bends' or 'turns' in the graph is&nbsp;[[0]].</p>\n<p></p>", "stepsPenalty": "1", "steps": [{"type": "information", "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>A degree $n$ polynomial has at most $n-1$ bends in its graph.</p>"}], "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "0", "maxValue": "0", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "contributors": [{"name": "Ben Brawn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/605/"}], "resources": []}]}], "contributors": [{"name": "Ben Brawn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/605/"}]}