How do I drop a function if it already exists?

This works for any object, not just functions:

IF OBJECT_ID('YourObjectName') IS NOT NULL 

then just add your flavor of object, as in:

IF OBJECT_ID('YourFunction') IS NOT NULL
   DROP FUNCTION YourFunction

You have two options to drop and recreate the procedure in SQL Server 2016.

Starting from SQL Server 2016 - use IF EXISTS

DROP FUNCTION [ IF EXISTS ] { [ schema_name. ] function_name } [ ,...n ]   [;]

Starting from SQL Server 2016 SP1 - use OR ALTER

CREATE [ OR ALTER ] FUNCTION [ schema_name. ] function_name   

IF EXISTS (
    SELECT * FROM sysobjects WHERE id = object_id(N'function_name') 
    AND xtype IN (N'FN', N'IF', N'TF')
)
    DROP FUNCTION function_name
GO

If you want to avoid the sys* tables, you could instead do (from here in example A):

IF object_id(N'function_name', N'FN') IS NOT NULL
    DROP FUNCTION function_name
GO

The main thing to catch is what type of function you are trying to delete (denoted in the top sql by FN, IF and TF):

• FN = Scalar Function
• IF = Inlined Table Function
• TF = Table Function

if object_id('FUNCTION_NAME') is not NULL
   DROP FUNCTION <name>

You can also look the name up in sysobjects

IF EXISTS (SELECT * 
       FROM   sysobjects 
           WHERE name='<function name>' and xtype='FN'

Actually, if the function could be a table function, you need to use

xtype in ('FN','TF')