Elementalist
I feel that the answer to this one depends on whether she is considered an equal member of the team, someone who may have their own limitations but is ultimately more or less just as valuable as everyone else, whatever the reason for that.
If she is then their relationship is going to be fairly normal because there won't be special treatment from the others (aside from thinking about her limitations when that's important) and there won't be any resentment from her feeling that she is inferior to others and treated as such.
If she isn't, well ... in that case it all depends on her character and on the situations she gets placed into and stuff, but ultimately people often start to feel resentment when they not only feel that they are inferior to others but are also treated as inferior. I will note, however, that if this is the case then the tone of the story should probably be what dictates the exact course of action, as a light-headed story probably shouldn't have an arc where things go to hell because a character goes rebellious from being treated badly by their team.
Edit: On a more personal note, I do have a character who could be considered a Badass Normal in one of my stories. She gets along fine due to the fact that instead of normal powers that everyone else has she has way weaker powers that normally aren't regarded as anything but allow her more flexibility than her teammates have (there's even a time when it clearly is what saves them), and because of the fact that she knows her stuff so she can teach someone who is a beginner to using powers how to do that. That said, she does have some issues with feeling inadequate, but those stem from the fact that she too was supposed to have powers of a similar kind as those of the team but she doesn't because they got sealed (think political hostage of a kind, it was supposed to stop someone from her family from doing ... not very ethical stuff), though it does cause her to do some really stupid stuff on occasions (say, like overusing her weaker version of what the other characters have when that requires use of her own blood to power it; there's a chapter that she spends doing nothing but getting carried and looking white as chalk because of this).
On a key note, monsters in my setting do require magic to deal with them, be it in-born magic or its way weaker blood magic equivalent that anyone (well, not really, there's some ... dark requirements) can learn, so for anyone aspiring to be important learning the latter if they have no former is required, so being able to use it does not preclude someone from being a Badass Normal in my setting.
edited 6th Jan '18 9:55:09 AM by Kazeto
My superhero story has plenty of Badass Normals in the Fantasy Kitchen Sink that is the world in this setting. However, one team is a group of teenage heroes known as the Future Fighters.
In a team that includes a shadowcaster (Noir), a water-manipulating Atlantean (Fathom), a speedster (Hyperactive), a Cyborg infused with alien nanomachines (Viral), a woman with spider powers (Arachna), a Human/Alai hybrid with a laser weapon and psionic abilities (Outlaw), and a mystic who summons beings to fight for her (Shy Child), the only member of the team with no powers is Comet. She's an Olympic-level athlete, a master archer, martial artist, bo staff user, and has a number of gadgets at her disposal. It also helps she comes from a rich family and helps the team out that way.
But how does one convincingly write The Team Normal in relation with her superpowered teammates? She's actually the fifth to join the team, the first four listed above are the founders, and she convinces them to allow her into their operations. Her family's money allows them a neat headquarters out of a warehouse, and she works very hard to keep up with the rest.
Any advice when it comes to writing the token Badass Normal of the team?