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This study aims to assess the understanding of the notion of function and the ability to articulate different semiotic registers for representation by new students in the university in Colombia. Immediate context is taken as the Faculty of Engineering at a public university. Epistemologically the study is based on symbolic interaction by analyzing the meanings that students attributed to this mathematical concept when addressing problem solving. The methodology, therefore, is qualitatively and use of theoretical coding is done. For analysis of the results it has been applied grounded theory with a structured approach. The information generated by this study corresponds to a test that showed students two graphic representations with the intent to identify which of them was a function, besides which should argue their response. Altogether 86 arguments around the concept are analyzed. Data analysis was done through atlas.ti 7.0 software. The system allows a glimpse of emerging categories the following findings: conceptual deficiencies, diversity in conceptual approaches, conceptual referents, semiotic representations, and finally highlight the various conceptual variations. [ABSTRACT FROM AUTHOR]