This study focuses on a case study that highlights the mathematical discourse developed by two pairs of students when dealing with a specific transition task, i.e., an activity leading to the construction of a graph of a function based on the exploration of another representation of the same function. Such a task was designed to work on the "transition beyond" that involves moving from the graph of a function in a dynamic geometry environment to the Cartesian graph of the same function in the paper-and-pencil environment. In this case study, I analyze in fine-grained detail the discourse developed by two pairs of high-school students (ages 15-16) and describe how they translate the dynamism of the proposed representation into the paper-based context. The analysis aims at investigating the potentialities of transition tasks for supporting the building of bridges between multiple representations of the same function. The analysis also showcased the important role dragging routines played for making the transition.