What Is a “Bonding Curve” and How Does It Relate to AMM Price Discovery?

A bonding curve is a mathematical function that defines the relationship between the supply of a token and its price. In an AMM, the constant product formula $x cdot y = k$ is a specific type of bonding curve.

The curve dictates that as more tokens are bought (increasing $y$ and decreasing $x$), the price of the token increases, and vice-versa. This function is the core of the AMM's automated price discovery.