This paper explores the application of resistive random-access memory (RRAM) devices in emulating various synapse functions. The electrical properties of an indium tin oxide (ITO)/SnOx/TaN device are examined, including the activation process, switching process, endurance (>102), and retention characteristics (104 s). A conduction mechanism for the resistive-switching process based on the migration of oxygen ions in the insulating SnOx film is proposed. Furthermore, the multilevel cell characteristics of the device, demonstrating the control of resistance states by variations in reset voltage and compliance current, were found to be suitable, increasing its data storage capacity. Synapse functions, including potentiation and depression, are tested, and their repeatability is evaluated. A neural network-based Modified National Institute Standards and Technology pattern recognition system is applied to the ITO/SnOx/TaN device, showcasing its capabilities in pattern recognition tasks. This study further explores various synapse functions, such as paired-pulse facilitation, paired-pulse depression, excitatory postsynaptic current, and activity-dependent synaptic plasticity. Hebbian learning rules, including spike rate-dependent plasticity, are demonstrated, along with spike time-dependent plasticity under various spike types, making it suitable for high-functionality neuromorphic applications. Finally, we assembled 3 × 3 synapse arrays and utilized them to form recognizable patterns, demonstrating the potential of the device in implementing neural network functions.