Characters as a function

Another character-writing muse from me, this one looking at how characters are created. As the title suggests, my characters are a function before they become a person. I think; what is their purpose in the story? Are they the hero, the brains behind the outfit, the helpful friend, a mentor figure? Once I've established their purpose in the story, I start to give them  a backstory and basic personality traits (although these can change, as I've said before, stories write themselves to a degree, so the personality I plan isn't always the one I go with). Sex is an interesting one; most of the time a character's sex is decided around the same time as their function (if they are a love interest, it's pretty important). But there is one character I have created who was planned to me male, but as I started putting the character together it made a lot more sense to make the character female, so she changed sex. Not everybody writes characters this way, and I am interested in seeing other peoples' creative process, because there have to be a lot of ways of building a character.