Well, it looks like Access can't do aggregates in UPDATE queries. But it can do aggregates in SELECT queries. So create a query with a definition like:
SELECT func_id, min(tax_code) as MinOfTax_Code
FROM Functions
INNER JOIN Tax
ON (Functions.Func_Year = Tax.Tax_Year)
AND (Functions.Func_Pure <= Tax.Tax_ToPrice)
GROUP BY Func_Id
And save it as YourQuery. Now we have to work around another Access restriction. UPDATE queries can't operate on queries, but they can operate on multiple tables. So let's turn the query into a table with a Make Table query:
SELECT YourQuery.*
INTO MinOfTax_Code
FROM YourQuery
This stores the content of the view in a table called MinOfTax_Code. Now you can do an UPDATE query:
UPDATE MinOfTax_Code
INNER JOIN Functions ON MinOfTax_Code.func_id = Functions.Func_ID
SET Functions.Func_TaxRef = [MinOfTax_Code].[MinOfTax_Code]
Doing SQL in Access is a bit of a stretch, I'd look into Sql Server Express Edition for your project!