A single synaptic device with inherent learning and memory functions is demonstrated based on an amorphous InGaZnO (a-IGZO) memristor; several essential synaptic functions are simultaneously achieved in such a single device, including nonlinear transmission characteristics, spike-rate-dependent and spike-timing-dependent plasticity, long-term/short-term plasticity (LSP and STP) and learning-experience behavior. These characteristics bear striking resemblances to certain learning and memory functions of biological systems. Especially, a learning-experience function is obtained for the first time, which is thought to be related to the metastable local structures in a-IGZO. These functions are interrelated: frequent stimulation can cause an enhancement of LTP, both spike-rate-dependent and spike-timing-dependent plasticity is the same on this point; and, the STP-to-LTP transition can occur through repeated stimulation training. The physical mechanism of device operation, which does not strictly follow the memristor model, is attributed to oxygen ion migration/diffusion. A correlation between short-term memory and ion diffusion is established by studying the temperature dependence of the relaxation processes of STP and ion diffusion. The realization of important synaptic functions and the establishment of a dynamic model would promote more accurate modeling of the synapse for artificial neural network.