This paper has two goals. The first is to present a model of the acquisition of a concept image of function. Theories describing the objectification of function are outlined through two different but related paths, and both stem from the conception of function as a process. The first path to objectification involves the generalization of the process view into one based on relationships between sets. The second path deals with function as an object possessing various properties, such as extrema and continuity. The second goal is to present the results of a year-long investigation on the acquisition of a function concept image in a high school Algebra II course which made significant use of the graphing calculator (GC). It was found that the students were able to define function objectively, but discussions and problem solving behaviors suggesting objectification occurred to a lesser degree. The graphic representation allowed objectification to occur more readily, and the use of the GC appeared to facilitate students' translation ability between functional representations. Students increased their use of the GC throughout the year, particularly on tasks which required graphical thinking. Misconceptions directly resulting from the use of the GC were also identified. (Contains 33 references.) (Author)