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The pathological behavior of strange functions has been of great help in the development and foundation of differential and integral calculus and, in general, of real analysis. In addition, it is a useful source of examples and counterexamples that help understand the rigorous definitions of the basic concepts of mathematical analysis. It is for this reason that the objective of this article is to study the properties of the Thomae function, and present some generalizations to guarantee differentiability on a considerably large set of points.