The objective of this paper is to study students' difficulties when they have to ascribe the same meaning to different representations of the same mathematical object. We address two theoretical tools that are at the core of Radford's cultural semiotic and Godino's onto-semiotic approaches: objectification and the semiotic function. The analysis of a teaching experiment involving high school students working on the tangent, shows how students' difficulties in ascribing sense to different representations of a common mathematical object can be traced back to the kind of objectification processes and semiotic functions they are able to establish.