In this paper, some aspects of the ideas of real function, continuous function, domain of a function and integral are investigated in the learning of mathematics, mainly referred to Italian High School (pupils aged 16-19 years); the status of these concepts in classroom practice is studied by some tests. The role of representations is important in the learning of mathematics; in particular, the influence of visualization is studied: the graphic representation (namely the Cartesian representation of a function) is often tacitly considered the main act of the study of a mathematical function; this procedure may be ineffective for the correct characterization of a concept and for the full development of the ability to use and to co-ordinate registers of representation.
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