We examine a prototype graphene field effect sensor for the study of the dielectric constant, pyroelectric coefficient, and ferroelectric polarization of 100-300 nm epitaxial (Ba,Sr)TiO3 thin films. Ferroelectric switching induces hysteresis in the resistivity and carrier density of n-layer graphene (n = 1-5) below 100 K, which competes with an antihysteresis behavior activated by the combined effects of electric field and temperature. We also discuss how the polarization asymmetry and interface charge dynamics affect the electronic properties of graphene.