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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.
97I20 Mappings and functions (educational aspects)
97I40 Differential calculus (educational aspects)
26A06 One-variable calculus
Full Text: DOI
[1] DOI: 10.4169/college.math.j.44.2.124 · Zbl 06222745 · doi:10.4169/college.math.j.44.2.124
[2] DOI: 10.1080/00207390802276218 · Zbl 1297.97020 · doi:10.1080/00207390802276218
[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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