Argumentation activities, such as constructing and communicating claims, critiquing others' ideas, and evaluating the strengths and weaknesses of claims, can play a foundational role in students' educational development. Yet there is more to understand about utilising these activities for effective mathematics learning. This paper discusses an exploration of 12 Australian students' responses to a purposefully designed argumentation task on graphing functions to provide insight into their attention to particular functions concepts. Issues related to argumentation task design and functions teaching and learning are discussed.