[[0]]
", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"vsetrangepoints": 5, "expectedvariablenames": [], "checkingaccuracy": 0.001, "vsetrange": [0, 1], "showpreview": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "answersimplification": "all", "scripts": {}, "answer": "(2x^2+({a}+{b}+1)x+{a}*{b}+{b}-{a}^2)/((x^2-{a}^2)(x+{b}))", "marks": 1, "checkvariablenames": false, "checkingtype": "absdiff", "type": "jme"}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}], "statement": "Turn the following expression into a single fraction whose denominator is in the simplest form possible.
\n\\[\\frac {1}{x-\\var{a}}+\\frac{1}{x^2-\\var{c}}+\\frac{1}{x+\\var{b}}\\]
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", "description": "Adding several rational functions.
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", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"allowFractions": true, "variableReplacements": [], "maxValue": "-{{a}+0.000001}", "minValue": "-infinity", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}], "statement": "Give an example of a value of $x$ where the function $f(x)=\\sqrt{\\simplify{x+{a}}}$ is not defined.
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", "description": "Find the domain of a function.
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\n$f(h(x))=\\;$ [[1]]
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\n$f(x)$=[[1]]
", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"allowFractions": true, "variableReplacements": [], "maxValue": "infinity", "minValue": "{a}+0.00001", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"allowFractions": true, "variableReplacements": [], "maxValue": "infinity", "minValue": "0.000001", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}], "statement": "Give an example of a value of $x$ where \\[f(x)=\\frac{1}{\\sqrt{x-\\var{a}}}\\] is defined and a possible value for $f(x).$
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", "description": "Finding domain and range of a given function.
", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}]}, {"name": "Functions: functional value ", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Sanka Balasuriya", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/738/"}], "functions": {}, "ungrouped_variables": ["a", "b", "c"], "tags": [], "preamble": {"css": "", "js": ""}, "advice": "", "rulesets": {}, "parts": [{"prompt": "$f(\\var{a})$ = [[0]]
", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"vsetrangepoints": 5, "expectedvariablenames": [], "checkingaccuracy": 0.001, "vsetrange": [0, 1], "showpreview": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "answersimplification": "all", "scripts": {}, "answer": "-{a}+{b}+{c}", "marks": 1, "checkvariablenames": false, "checkingtype": "absdiff", "type": "jme"}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}], "statement": "Find $f(\\var{a})$ if $f(x)=\\big| \\; |-x+\\var{b}|-\\var{c}\\big|,$ where $|x|$ denote the absolute value of $x.$
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", "description": "Functional value of a function at a point.
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", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"vsetrangepoints": 5, "expectedvariablenames": [], "checkingaccuracy": 0.001, "vsetrange": [0, 1], "showpreview": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "answersimplification": "all", "scripts": {}, "answer": "{p}^3+{a}*{p}^2+{b}*{p}+{c}", "marks": 1, "checkvariablenames": false, "checkingtype": "absdiff", "type": "jme"}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}], "statement": "Evaluate $f(x)=\\simplify{x^3+{a}*x^2+{b}*x+{c}}$ at $x=\\var{p}.$
", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"a": {"definition": "random(1..5)", "templateType": "anything", "group": "Ungrouped variables", "name": "a", "description": ""}, "p": {"definition": "random(1..3)", "templateType": "anything", "group": "Ungrouped variables", "name": "p", "description": ""}, "c": {"definition": "random(1..5)", "templateType": "anything", "group": "Ungrouped variables", "name": "c", "description": ""}, "b": {"definition": "random(1..5)", "templateType": "anything", "group": "Ungrouped variables", "name": "b", "description": ""}}, "metadata": {"notes": "Evaluating functions.
", "description": "Calculate the functional value at a point.
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