Understanding the behavior of functions as they approach infinity is crucial in calculus. Infinity is not a number; instead, we analyze limits as x approaches infinity. An increasing function's limit at infinity may not necessarily be infinity, as demonstrated by the example f(x) = (x - 1)/x, which approaches 1. The discussion also highlights that the concept of "function pattern" needs clarification, as it relates to the behavior of functions on the Cartesian system. Ultimately, calculus provides tools like derivatives to determine whether a function is increasing or decreasing at specific points.