FAQ : What is Partition Function in SQL Server?

Partition functions are special kind of objects (of course created by user) created in a database which can be used only by partition scheme. Partition function contains a data type , that must be the same data type as the partition column chosen in the table. Partition Function as such not directly related to any table.

NOTE: Even though Partition Function to Partition scheme is One to Many, in sliding window scenario moving data between in and out of partition is a common requirement, which require Partition function modification. So practically it makes each Partition table should have exclusive partition function and scheme.
Partition functions are not user defined functions.

Here are few of facts to be known about partition functions• Partition functions are not listed as database objects in the sys.all_objects or sys.objects system tables; instead, you can find them listed in sys.partition_functions.
• Partition functions are not contained by a database schema.
• Special commands must be used for creating, altering, and dropping a partition function:
o CREATE PARTITION FUNCTION
o ALTER PARTITION FUNCTION
o DROP PARTITION FUNCTION
• Partition functions can be invoked interactively in Transact-SQL by using the $PARTITION function.

Partition Functions System Objects

• sys.partition_functions : Contains a row for each partition function.
• sys.partition_range_values : Contains a row for each range boundary value of a partition function of type R.
• sys.partition_parameters : Contains a row for each parameter of a partition function.
• $PARTITION. :Returns the partition number into which a set of partitioning column values would be mapped for any specified partition function.
Eg. SELECT $PARTITION.RangePF1 (10) ;