This study investigates prospective teachers' understanding of the connections between algebraic and graphical representations of the functions and their development of the concept via process-object conceptions in each of these situations. The results indicated that most of the participants were dependent upon an algebraic expression to think about a function and use it in the processes of derivative and integral. Development of a process conception of function appears to be more complicated than it is considered. The participants successfully employed this quality of thinking when the situation was familiar to them; yet they had great struggle to cope with a function process when they were given an unfamiliar situation. The research findings also suggest that the possession of an object conception of function could enable one to move freely between algebraic and graphical representations. On the other way around, students' capability at shifting between algebraic and graphical representations of the functions appear to be crucial stage to develop an object conception of function. (Contains 6 tables and 8 figures.)