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Rotating real-valued functions in the plane. (English) Zbl 1337.97011
Summary: Let \(f\) be a real-valued function defined over a subset of \(\mathbb{R}\). In the following article, we investigate the graph of \(f\) under rotation by a fixed angle about the origin. In particular, we give necessary and sufficient conditions on the angles of rotation which result in an image that still describes a function. We include several illuminating examples and use the converse of the mean value theorem to extend previously known results.
MSC:
97I20 Mappings and functions (educational aspects)
97I40 Differential calculus (educational aspects)
26A06 One-variable calculus
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[1] DOI: 10.4169/college.math.j.44.2.124 · Zbl 06222745 · doi:10.4169/college.math.j.44.2.124
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[3] DOI: 10.1080/0020739X.2010.500697 · Zbl 1273.97035 · doi:10.1080/0020739X.2010.500697
[4] DOI: 10.2307/2974475 · Zbl 0901.26004 · doi:10.2307/2974475
[5] DOI: 10.1007/b97662 · doi:10.1007/b97662
[6] Rudin W, Principles of mathematical analysis., 3. ed. (1976) · Zbl 0346.26002
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