The concept of function is fundamental importance to the mathematics. Since the most mathematical concept is not acquired in one step [13], thus we have to take a long journey for developing of the function concept. One of the aim of this process to develop an effective concept image which have an important role in problem solution. The students decides on the basis of a concept image whether a given mathematical object is an example or nonexample of the concept. (Vinner & Dreyfus, 1989). In this paper we are looking for the answer of the following question: what are the concept image of the function concept formed of the students by the end of the primary school (8th grade) and the first year engineering university students?