// Numbas version: exam_results_page_options
{"name": "Is this a function?", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"metadata": {"licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International", "description": "<p>Given an equation or a worded&nbsp;formula determine if it is a function or not</p>"}, "extensions": [], "rulesets": {}, "advice": "<p>A function is a rule that assigns at most one output&nbsp;for each input.</p>\n<p></p>\n<p>For an equation such as $y=x^2+3$, we think of $x$ as the input and $y$ as the output. Since each $x$ gives at most one $y$ value this is a function.</p>\n<p></p>\n<p>Since&nbsp;things such as $y&gt;x$,&nbsp;$y=\\pm\\sqrt{x}$ and '$y=2 \\text{ and } 3x $' give more than one $y$ value for an $x$ value these are not functions.</p>\n<p></p>\n<p>Graphically, the requirement that there is at most one $y$ value for each $x$ value means a curve is the graph of a function if it passes the 'vertical line test'. That is, if you draw vertical lines through&nbsp;the graph and&nbsp;each vertical line only cuts the graph at most once, the graph 'passes' the vertical line test and it represents a function.</p>\n<p></p>", "name": "Is this a function?", "tags": [], "ungrouped_variables": ["n", "equationlist", "wordlist"], "statement": "<p>Are the following, functions or not?</p>\n<p></p>", "variables": {"wordlist": {"templateType": "anything", "name": "wordlist", "definition": "shuffle([\n    random(\n  ['Given an input, the output is a number \\$\\\\var{n[8]}\\$ times the input and another number that was the input',0,1],\n  ['Given an input, the output is the number \\$\\\\var{n[13]}\\$ and the number \\$\\\\var{n[14]}\\$',0,1]  \n    ),\n    random(['You input a number and you get an output of \\$\\\\var{abs(n[9])}\\$ less than the input',1,0],\n  ['You input a number and you get an output of \\$\\\\var{abs(n[12])}\\$ more than the input',1,0]\n)])", "group": "Ungrouped variables", "description": ""}, "equationlist": {"templateType": "anything", "name": "equationlist", "definition": "shuffle([\n    random(\n  ['\\$y=\\\\simplify{{n[0]}x^{{n[1]}}+{n[2]}\\}\\$',1,0] ,\n  ['\\$f(x)=\\\\var{n[3]}\\$',1,0],\n  ['\\$y=\\\\sqrt{\\\\simplify{{abs(n[6])}x+{n[7]}}}\\$',1,0],\n   ['\\$y=-\\\\sqrt{\\\\simplify{{-abs(n[15])}x+{n[16]}}}\\$',1,0],\n  ['\\$y=\\\\var{n[10]}x\\$ and \\$\\\\var{n[11]}x\\$',0,1],\n  ['\\$y=\\\\pm \\\\sqrt{\\\\simplify{{abs(n[4])}x+{n[5]}}}\\$',0,1]\n ), \n   random( \n  ['\\$y>\\\\simplify{{n[13]}x+{n[14]}\\}\\$', 0,1],\n  ['\\$y\\\\leq\\\\simplify{{n[13]}x+{n[14]}\\}\\$', 0,1],\n  ['\\$y<\\\\simplify{{n[13]}x+{n[14]}\\}\\$', 0,1],\n  ['\\$y\\\\ge\\\\simplify{{n[13]}x+{n[14]}\\}\\$',0,1]\n)\n])", "group": "Ungrouped variables", "description": "<p>want to choose some of these randomly each time...</p>"}, "n": {"templateType": "anything", "name": "n", "definition": "shuffle(-10..10 except 0)", "group": "Ungrouped variables", "description": ""}}, "variable_groups": [], "variablesTest": {"condition": "", "maxRuns": 100}, "preamble": {"css": "", "js": ""}, "parts": [{"maxMarks": 0, "showFeedbackIcon": true, "type": "1_n_2", "scripts": {}, "marks": 0, "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "matrix": "equationlist[0][1..3]", "prompt": "<p>{equationlist[0][0]}</p>\n<p></p>", "shuffleChoices": false, "choices": ["<p>Function</p>", "<p>Not a function</p>"], "displayColumns": 0, "displayType": "radiogroup", "minMarks": 0, "variableReplacements": []}, {"maxMarks": 0, "showFeedbackIcon": true, "type": "1_n_2", "scripts": {}, "marks": 0, "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "matrix": "equationlist[1][1..3]", "prompt": "<p>{equationlist[1][0]}</p>", "shuffleChoices": false, "choices": ["<p>Function</p>", "<p>Not a function</p>"], "displayColumns": 0, "displayType": "radiogroup", "minMarks": 0, "variableReplacements": []}, {"maxMarks": 0, "showFeedbackIcon": true, "type": "1_n_2", "scripts": {}, "marks": 0, "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "matrix": "wordlist[0][1..3]", "prompt": "<p>{wordlist[0][0]}</p>", "shuffleChoices": false, "choices": ["<p>Function</p>", "<p>Not a function</p>"], "displayColumns": 0, "displayType": "radiogroup", "minMarks": 0, "variableReplacements": []}, {"maxMarks": 0, "showFeedbackIcon": true, "type": "1_n_2", "scripts": {}, "marks": 0, "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "matrix": "wordlist[1][1..3]", "prompt": "<p>{wordlist[1][0]}</p>", "shuffleChoices": false, "choices": ["<p>Function</p>", "<p>Not a function</p>"], "displayColumns": 0, "displayType": "radiogroup", "minMarks": 0, "variableReplacements": []}], "functions": {}, "type": "question", "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/"}]}