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Assuming there are three functions:
Ultra function

Super function

Ultimate function

When you mention these, which is/are correct?

There are the Ultra, Super, Ultimate functions.

There are the Ultra, Super, Ultimate function.

There are three functions, the Ultra, Super, and the Ultimate functions.

There are three functions, the Ultra, Super, and the Ultimate function.

There are three functions as follows: The Ultra, and Super, and the Ultimate function.

There are the Ultra, Super, and the Ultimate function.

I think 4, 5,6th are correct.

Thanks
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The correct sequences are:

There are three functions: the Ultra, the Super and the Ultimate.
There are three functions: an Ultra function, a Super function, and an Ultimate function.
You can add "as follows:" after "functions".
Comments  
Two lines are really understandable! 
THanks, AlpheccaStars.