Which two functions are performed by the core layer in a three-tier architecture?

Cisco is very clear about the purpose of this layer. Its only role is to forward traffic, the fastest it can. Here you don’t apply any policy, as you must try to reduce the load of the core so it can focus on routing.

https://www.cisco.com/c/en/us/td/do cs/solutions/Enterprise/Campus/campover.html#wp708831