This article reports on the understanding of the function concept by pre-service mathematics teachers from two countries (Germany and Croatia). We focused on investigating students' concept definition and concept image of the function in relation to their curriculum experiences. Data were collected using a questionnaire in the form of open-ended questions followed by interviews. The results indicate that the curriculum has a great influence on the development of the concept definition and concept image. The curriculum strongly influenced the theoretical background of the function concept and thus the gap between the formal and the personal definition of function. Later and more intensive work with the formal definition of function led to a better development of the function concept in general. The curriculum also had an influence on the range of the concept image developed by the pre-service mathematics teachers, with no proportional dependence in relation to the better developed understanding of the concept of function.