While the concept of function has been extensively studied by researchers worldwide, there has been limited research conducted on this topic in Sweden. This paper aims to fill this gap by examining the significance of critical aspects and their impact on mathematical communication. The study analyzes the content presented to students regarding the concept of function, both in the classroom and through textbooks, and compares it to the actual learning outcomes. Data for the analysis was collected from two classes, involving two teachers and 45 students, including video recordings of lessons and tests. The analytical framework incorporates concepts from variation theory. The findings highlight that effective communication in the classroom hinges on considering critical aspects as the foundation of students’ learning. In this study, the argument of functions is identified as a crucial aspect in understanding functions.