Query below return all User Defined Functions and information about it in Azure SQL database.
Query
select schema_name(obj.schema_id) as schema_name,
       obj.name as function_name,
       case type
            when 'FN' then 'SQL scalar function'
            when 'TF' then 'SQL inline table-valued function'
            when 'IF' then 'SQL table-valued-function'
        end as type,
        substring(par.parameters, 0, len(par.parameters)) as parameters,
        TYPE_NAME(ret.user_type_id) as return_type,
        mod.definition
from sys.objects obj
join sys.sql_modules mod
     on mod.object_id = obj.object_id
cross apply (select p.name + ' ' + TYPE_NAME(p.user_type_id) + ', ' 
             from sys.parameters p
             where p.object_id = obj.object_id 
                   and p.parameter_id != 0 
            for xml path ('') ) par (parameters)
left join sys.parameters ret
          on obj.object_id = ret.object_id
          and ret.parameter_id = 0
where obj.type in ('FN', 'TF', 'IF')
order by schema_name,
         function_name;
Columns
- schema_name - schema name
- function_name - function name
- type - type of UDF:
- SQL scalar function
- SQL inline table-valued function
- SQL table-valued-function
 
- parameters - name of parameters and their data types
- return_type - for scalar function data type of returning scalar value
- definition - function definition (CREATE FUNCTION statement)
Rows
- One row represents one function
- Scope of rows: all user defined functions in database
- Ordered by schema name and function name
Sample results

 
                                                                     
                                                                     
                                                                     
                                                                     
                                                                     
                                                                     
                                                                     
                                                                     
                                                                     
                                                                     
                                                                     
                                                                     
                                                                     
                                                                     
                                                                     
                                                                     
                                                                     
                                                                 
                                                             
                                                             
                                                             
                                                             
                                                                 
                                                             
                                                             
                                                                 
                                                             
                                                             
                                                             
                                                             Bart Gawrych
                                                                        Bart Gawrych
                                 Azure SQL Database
                                                                Azure SQL Database
                                 SQL Server
                                                                                                SQL Server
                                             Oracle database
                                                                                                Oracle database
                                             Snowflake
                                                                                                Snowflake
                                             IBM Db2
                                                                                                IBM Db2
                                             Teradata
                                                                                                Teradata
                                             Vertica
                                                                                                Vertica
                                             PostgreSQL
                                                                                                PostgreSQL