We have fabricated a centimeter-size single-layer graphene device with a gate electrode, which can modulate the transmission of terahertz and infrared waves. Using time-domain terahertz spectroscopy and Fourier-transform infrared spectroscopy in a wide frequency range (10-10 000 cm(-1)), we measured the dynamic conductivity change induced by electrical gating and thermal annealing. Both methods were able to effectively tune the Fermi energy, E(F), which in turn modified the Drude-like intraband absorption in the terahertz as well as the "2E(F) onset" for interband absorption in the mid-infrared. These results not only provide fundamental insight into the electromagnetic response of Dirac fermions in graphene but also demonstrate the key functionalities of large-area graphene devices that are desired for components in terahertz and infrared optoelectronics.