Rotating real-valued functions in the plane

Abstract

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.

Keywords:

• differentiable functions
• plane rotation
• mean value theorem

2010 Mathematics Subject Classification:

• Primary 26A06
• Secondary 26A24

Acknowledgements

The authors wish to thank the referees for their helpful comments and suggestions.

Disclosure statement

No potential conflict of interest was reported by the authors.