Infinite limit of a function at infinity and its phenomenology

In this paper we aim to characterise and define the phenomena of the infinite limit of a function at infinity. Based on the intuitive and formal approaches, we obtain as results five phenomena organised by a definition of this limit: intuitive unlimited growth of a function, for plus and minus infinity, and intuitive unlimited decrease of a function, for plus and minus infinity (intuitive approach), and the round-trip phenomenon of infinite limit functions (formal approach). All this is intended to help overcome the difficulties that pre-university students have with the concept of limit, contributing from phenomenology, Advanced and Elementary Mathematical Thinking, and APOS theory. Keywords: limit, infinity, functions, phenomenology, Advanced Mathematical Thinking, APOS