// Numbas version: exam_results_page_options
{"name": "Graphing: linear", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"functions": {}, "ungrouped_variables": ["a", "b", "lleading", "rleading", "xints"], "name": "Graphing: linear", "tags": ["graphing", "linear", "polynomials", "sketching", "straight lines"], "preamble": {"css": "", "js": ""}, "advice": "", "rulesets": {}, "parts": [{"stepsPenalty": "1", "displayColumns": 0, "prompt": "<p>This equation, or its graph, can be described as a</p>", "matrix": ["1", "0", "0", 0, 0, 0], "shuffleChoices": true, "maxMarks": 0, "variableReplacements": [], "choices": ["<p>straight line</p>", "<p>parabola/quadratic</p>", "<p>cubic</p>", "<p>hyperbola</p>", "<p>circle</p>", "<p>quartic</p>"], "variableReplacementStrategy": "originalfirst", "steps": [{"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>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "distractors": ["", "", "", "", "", ""], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "1_n_2", "displayType": "radiogroup", "minMarks": 0}, {"stepsPenalty": "1", "displayColumns": 0, "prompt": "<p>As we move to the far left of the graph, the graph</p>", "matrix": "lleading", "shuffleChoices": false, "maxMarks": 0, "variableReplacements": [], "choices": ["<p>goes upwards.</p>", "<p>goes downwards.</p>"], "variableReplacementStrategy": "originalfirst", "steps": [{"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>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "1_n_2", "displayType": "radiogroup", "minMarks": 0}, {"stepsPenalty": "1", "displayColumns": 0, "prompt": "<p>As we move to the far right&nbsp;of the graph, the graph</p>", "matrix": "rleading", "shuffleChoices": false, "maxMarks": 0, "variableReplacements": [], "choices": ["<p>goes upwards.</p>", "<p>goes downwards.</p>"], "variableReplacementStrategy": "originalfirst", "steps": [{"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>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "1_n_2", "displayType": "radiogroup", "minMarks": 0}, {"stepsPenalty": "1", "prompt": "<p>The $y$-intercept of the graph is $y=$[[0]].</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "steps": [{"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>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "gaps": [{"allowFractions": true, "variableReplacements": [], "maxValue": "{b}", "minValue": "{b}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": true, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"stepsPenalty": "1", "prompt": "<p>The set of $x$-intercepts of the graph&nbsp;would be&nbsp;[[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>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "steps": [{"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>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "gaps": [{"vsetrangepoints": 5, "expectedvariablenames": [], "checkingaccuracy": 0.001, "vsetrange": [0, 1], "showpreview": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "answer": "{xints}", "marks": 1, "checkvariablenames": false, "checkingtype": "absdiff", "type": "jme"}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"stepsPenalty": "1", "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>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "steps": [{"prompt": "<p>A degree $n$ polynomial has at most $n-1$ bends in its graph.</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "gaps": [{"allowFractions": false, "variableReplacements": [], "maxValue": "0", "minValue": "0", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}], "extensions": [], "statement": "<p>You are given the equation&nbsp;$y=\\simplify[all,fractionNumbers]{{a}x+{b}}$.&nbsp;</p>", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"a": {"definition": "random(-6..6 except 0)", "templateType": "anything", "group": "Ungrouped variables", "name": "a", "description": ""}, "lleading": {"definition": "[if(a<0,1,0),if(a<0,0,1)]", "templateType": "anything", "group": "Ungrouped variables", "name": "lleading", "description": ""}, "b": {"definition": "random(-10..10)", "templateType": "anything", "group": "Ungrouped variables", "name": "b", "description": ""}, "rleading": {"definition": "[if(a>0,1,0),if(a>0,0,1)]", "templateType": "anything", "group": "Ungrouped variables", "name": "rleading", "description": ""}, "xints": {"definition": "set(-b/a)", "templateType": "anything", "group": "Ungrouped variables", "name": "xints", "description": ""}}, "metadata": {"description": "", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}], "contributors": [{"name": "Ben Brawn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/605/"}]}]}], "contributors": [{"name": "Ben Brawn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/605/"}]}