In an automated market maker, price follows the relationship between assets in a pool. Each trade changes that relationship. The smaller the pool relative to an order, the larger the difference between the pre-trade price and execution can be.
Read liquidity, volume and pair age together. High volume against little liquidity does not automatically describe a healthy market.
Liquidity can be split across pools and exchanges. An aggregate is a shortcut, but a fresh quote and minimum received matter before a larger order. A deep pool does not verify a project.