I need to figure out the last time that a function was used by SQL Server. How can I do this?
You can use Change Data Capture or Change tracking to analyse the required changes here

You might need to drill down more with Sql server audit to capture the required use for the function in question SQL Server Audit Action Groups and Actions

Also,

You can get a possible idea as mentioned here:using below query

SELECT usecounts
FROM sys.dm_exec_cached_plans 
CROSS APPLY sys.dm_exec_sql_text(plan_handle) 
WHERE sys.dm_exec_sql_text.objectid=object_id('YourFunction') 


So basically you have to find a proper way to analyse the usage.