What we are calling a"monotonic transformation" is, strictly speaking, called a "positive monotonic transformation", in order to distinguish
it from a "negative montonic transformation", which is one that reverses the order of numbers.
Monotonic transformations are sometimes called "monotonous tranformations", which seems unfair, since they can actually be quite interesting.
From Varian, H. R., & Repcheck, J. (2006). Intermediate microeconomics: a modern approach, p: 56. Utility.