// Numbas version: exam_results_page_options {"name": "Joshua's copy of Domain of a piecewise function", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"extensions": [], "tags": [], "metadata": {"licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International", "description": "

Multiple choice question. Given a randomised polynomial select the possible ways of writing the domain of the function.

"}, "ungrouped_variables": ["a", "b", "c", "d", "b0", "b1", "b2", "Answer1", "Answer2", "Input1", "Input2"], "statement": "

Given the real function below, you should be able to determine its domain.

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\\simplify{f}(\\simplify{t})=\\left\\{\\begin{align}&\\simplify{0},&& \\text{ for } \\simplify{x}< \\var{b0}, \\\\&\\simplify{{a}x+{b}},&& \\text{ for } \\var{b0}\\leq \\simplify{x}< \\var{b1},\\\\ &\\simplify{{c}x^2+{d}},&& \\text{ for } \\var{b1}\\leq\\simplify{x}< \\var{b2},\\end{align}\\right.

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What is the value of $f(\\var{Input1})$? [[0]]

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What is the value of $f(\\var{Input2})$? [[1]]

The function $\\simplify{{out}}$ is a piecewise function. It is defined on different parts (or pieces) of its domain by different (sub)functions.

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In particular, the pieces of the domain are the intervals

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• $\\simplify{{inp}}< \\var{b0}$
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• $\\var{b0}\\leq \\simplify{{inp}}\\leq \\var{b1}$,
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• $\\var{b2}\\leq\\simplify{{inp}}< \\var{b3}$,
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• $\\var{b3}<\\simplify{{inp}}\\leq \\var{b4}$ and
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• $\\simplify{{inp}}\\ge\\var{b5}$.
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and their corresponding (sub)functions are given by the expressions

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• $\\simplify{{p0}}$
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• $\\simplify{{p1}}$
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• $\\simplify{{p2}}$
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• $\\simplify{{p3}}$
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• $\\simplify{{p4}}$
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In the case of the function $\\simplify{{out}}$ above, each of the (sub)functions are defined for the indicated intervals and so the domain of $\\simplify{{out}}$ are all of those intervals combined. The first and second interval join nicely without a gap unlike the rest and so we have \$\\text{dom}(\\simplify{{out}})=\\{\\simplify{{inp}}\\in\\mathbb{R}:\\, \\simplify{{inp}}\\leq \\var{b1},\\; \\var{b2}\\leq \\simplify{{inp}}<\\var{b3},\\; \\var{b3}<\\simplify{{inp}}\\leq\\var{b4}, \\text{ or }\\; \\simplify{{inp}}\\ge \\var{b5}\\}.\$

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", "type": "question", "contributors": [{"name": "Ben Brawn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/605/"}, {"name": "Joshua Calcutt", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3267/"}]}]}], "contributors": [{"name": "Ben Brawn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/605/"}, {"name": "Joshua Calcutt", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3267/"}]}