DOMAIN, CO-DOMAIN AND RELATIONSHIP: THREE EQUALLY IMPORTANT ASPECTS OF A CONCEPT IMAGE OF FUNCTION

Students ' concept images of function often lack in understanding the concept as inextricably connected with its domain, co-domain and relationship. The impact of this on understanding properties such as 1-1 can be dramatic. Drawing on students' responses to a task involving the exploration of whether five given functions were 1-1, onto, both or neither, I discuss the following distinctive elements in their responses: A. use of graphs to identify properties of the function (from relying completely on the graph for mere identification of the property through to substantiating what the graph suggests with verbal explanations and uses of B and C) B. problematic uses of the formal definitions of 1-1 and onto C. effective use of properties specific to the functions in question (e.g. uniqueness of cubic root). The emphasis here is on B. Studies of perceptions of function that focus on difficulties the students encounter when they are asked to decide whether a given relationship or a graph represents a function (e.g. Barnes 1988) date back in the 1980s when this concept became a well-studied area of upper secondary and tertiary mathematics education. In these studie