Yes these functions exist. Both theoretically and practically. These are the supply and demand curves and it can be measured. You can then derive functions from

Yes these functions exist. Both theoretically and practically. These are the supply and demand curves and it can be measured. You can then derive functions from the measurements, with the shape of that function defining different types of market behavior. The inputs of that function are in principal simple and answers the question how does price change as the supply and demand of a good changes? (or the inverse - how does demand change as the price changes?)