Reservoir computing (RC) is an energy-efficient computational framework with low training cost and high efficiency in processing spatiotemporal information. The state-of-the-art fully memristor-based hardware RC system suffers from bottlenecks in the computation efficiencies and accuracy due to the limited temporal tunability in the volatile memristor for the reservoir layer and the nonlinearity in the nonvolatile memristor for the readout layer. Additionally, integrating different types of memristors brings fabrication and integration complexities. To overcome the challenges, a multifunctional multi-terminal electrolyte-gated transistor (MTEGT) that combines both electrostatic and electrochemical doping mechanisms is proposed in this work, integrating both widely tunable volatile dynamics with high temporal tunable range of 10² and nonvolatile memory properties with high long-term potentiation/long-term depression (LTP/LTD) linearity into a single device. An ion-controlled physical RC system fully implemented with only one type of MTEGT is constructed for image recognition using the volatile dynamics for the reservoir and nonvolatility for the readout layer. Moreover, an ultralow normalized mean square error of 0.002 is achieved in a time series prediction task. It is believed that the MTEGT would underlie next-generation neuromorphic computing systems with low hardware costs and high computational performance.