This paper deals with three classes of functions of great importance in analysis and its applications. We construct a family
of Hlder functions in the closed unit interval having two continuous parameters. Those functions are not of bounded variation
for any pair of values of the Hlder constant and exponent. The construction depends on a change of variables given by a Lipschitz
function with constant equal to 1. Several questions related to the concepts of genericity, surjectivity and deformability
are posed at the end.