The limit value of a function is a fundamental mathematical notion that describes how a function behaves close to a given point lim𝑥→𝑥0 𝑓(𝑥). We first met the limits of a function in high school mathematics classes, and we later applied it in various areas, most notably physics. Understanding the concept of a function's limit value is far from straightforward. There are no universal rules, although visualization can be an effective technique for overcoming difficulties in this procedure. This work presents an idea for visualization through a physical experiment. An example of measuring the acceleration of the system using Atwood's machine was presented. The system consists of a pulley of radius R and mass M, and two objects with masses 𝑚1 and 𝑚2 that are connected by an inextensible massless string. The acceleration of the system is measured for the variable mass 𝑚2 and behavior of the function 𝑎(𝑚2 ) at infinity (𝑚2 → +∞) is examined. The graphical presentation of the results illustrates that the limit value of the function gives the horizontal asymptote 𝑎 = 𝑔. The proposed concept would enable the introduction of more effective visual learning strategies not only in the teaching of mathematics but also in other natural sciences.