// Numbas version: finer_feedback_settings
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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>", "rulesets": {}, "extensions": [], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true, "j": false}, "constants": [], "variables": {"wordlist": {"name": "wordlist", "group": "Ungrouped variables", "definition": "shuffle([\n    random(      \n  ['For each input, the output will be two numbers, one will be \\$\\\\var{n[8]}\\$ times the input and the other will be \\$\\\\var{n[9]}\\$ times the input.',0,1,'This is not a function since the output contains more than one number.'],\n  ['For each input, the output will be two numbers, one will be \\$\\\\var{n[10]}\\$ times the input and the other number will be \\$\\\\var{n[11]}\\$.',0,1,'This is not a function since the output contains more than one number.']  \n    ),\n    random(['You input a number and you get an output of \\$\\\\var{abs(n[9])}\\$ less than the input.',1,0,'This is a function since for each input there is a single output.'],\n  ['You input a number and you get an output of \\$\\\\var{abs(n[12])}\\$ more than the input.',1,0,'This is a function since for each input there is a single output.']\n)])", "description": "", "templateType": "anything", "can_override": false}, "equationlist": {"name": "equationlist", "group": "Ungrouped variables", "definition": "shuffle([\n    random(\n  ['\\$y=\\\\simplify{{n[0]}x^{{n[1]}}+{n[2]}\\}\\$',1,0, 'This is a function of \\$x\\$. For each \\$x\\$ the result of the right-hand side of the equation is a single number \\$y\\$.'] ,\n  ['\\$f(x)=\\\\var{n[3]}\\$',1,0, 'This is a function of \\$x\\$. For each \\$x\\$ the result of the right-hand side of the equation is a single number \\$f(x)\\$.'],\n  ['\\$y=\\\\sqrt{\\\\simplify{{abs(n[6])}x+{n[7]}}}\\$',1,0, 'This is a function of \\$x\\$. For each \\$x\\$ in the domain, the result of the right-hand side of the equation is a single number \\$y\\$.'],\n   ['\\$y=-\\\\sqrt{\\\\simplify{{-abs(n[15])}x+{n[16]}}}\\$',1,0, 'This is a function of \\$x\\$. For each \\$x\\$ in the domain, the result of the right-hand side of the equation is a single number \\$y\\$.'],\n  ['\\$y=\\\\var{n[10]}x\\$ and \\$\\\\var{n[11]}x\\$',0,1, 'This is not a function of \\$x\\$. For each \\$x\\$ we have two corresponding \\$y\\$ values.'],\n  ['\\$y=\\\\pm \\\\sqrt{\\\\simplify{{abs(n[4])}x+{n[5]}}}\\$',0,1, 'This is not a function of \\$x\\$. For each \\$x\\$ we have two corresponding \\$y\\$ values (a positive and a negative value).']\n ), \n   random( \n  ['\\$y>\\\\simplify{{n[13]}x+{n[14]}\\}\\$', 0,1, 'This is not a function of \\$x\\$. For each \\$x\\$ we have more than one corresponding \\$y\\$ value (we actually have an infinite number of them).'],\n  ['\\$y\\\\leq\\\\simplify{{n[13]}x+{n[14]}\\}\\$', 0,1, 'This is not a function of \\$x\\$. For each \\$x\\$ we have more than one corresponding \\$y\\$ value (we actually have an infinite number of them).'],\n  ['\\$y<\\\\simplify{{n[13]}x+{n[14]}\\}\\$', 0,1, 'This is not a function of \\$x\\$. For each \\$x\\$ we have more than one corresponding \\$y\\$ value (we actually have an infinite number of them).'],\n  ['\\$y\\\\ge\\\\simplify{{n[13]}x+{n[14]}\\}\\$',0,1, 'This is not a function of \\$x\\$. For each \\$x\\$ we have more than one corresponding \\$y\\$ value (we actually have an infinite number of them).']\n)\n])", "description": "<p>want to choose some of these randomly each time...</p>", "templateType": "anything", "can_override": false}, "n": {"name": "n", "group": "Ungrouped variables", "definition": "shuffle(-10..10 except 0)", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["n", "equationlist", "wordlist"], "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, 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