Functions in a function app share resources. Among those shared resources are connections: HTTP connections, database connections, and connections to services such as Azure Storage.
The potentiel issue
The method to avoid to use more connections that we need
We can reuse client instances rather than creating new ones with each function invocation : use a single static client (for example, .NET clients - HttpClient, DocumentClient, Azure Storage Clients,…).
Example with Http request
Example with zure Cosmos DB client