Understanding the relationship between the topology of a network and its function remains an important question in biological physics. However, this is not a one-to-one mapping. Often the behavior of a signaling system varies with the input signal it receives. For example, some biological systems show adaptation when they receive a low input signal while they show oscillation with a high input signal. We therefore set out to find all possible two-node and three-node networks that can perform both adaptation and oscillation with transcriptional regulation and enzymatic reactions. For two-node networks, we identified all bi-functional topologies by analyzing the Jacobean matrix. For three-node networks, they were identified by enumeration. We further investigated how the system can be transformed between these two functions. We found that the switching of functions can be achieved through changing anyone of the several key parameters, including the input signal level.