Graphene-based devices are planned to augment the functionality of Si and III-V based technology in radio-frequency (RF) electronics. The expectations in designing graphene field-effect transistors (GFETs) with enhanced RF performance have attracted significant experimental efforts, mainly concentrated on achieving high mobility samples. However, little attention has been paid, so far, to the role of the access regions in these devices. Here, we analyse in detail, via numerical simulations, how the GFET transfer response is severely impacted by these regions, showing that they play a significant role in the asymmetric saturated behaviour commonly observed in GFETs. We also investigate how the modulation of the access region conductivity (i.e., by the influence of a back gate) and the presence of imperfections in the graphene layer (e.g., charge puddles) affects the transfer response. The analysis is extended to assess the application of GFETs for RF applications, by evaluating their cut-off frequency.