Q:

Activate a function every day to check week

I want to make a schedule app. To do this I need to separate each week, since the schedule is different(ex:week 1 is week A, week 2 is week B, week 3 is week a). 
I need to make a function that will run every day that will determine which week it is. I have a abstract idea on what the function will look like, just that I do not know what to pass into the function, as well as how to run this function every day without the user doing anything.
Heres a bit of what I am thinking.
func DetermineIfWeekA(n:IntMax;something )-> Bool{
for k in 0...n{
    if (DayDifference == 14*k+3,14*k+4,14*k+5,14*k+6,14*k+7){
        return true
    }else if(DayDifference == 14*k+10,14*k+11,14*k+12,14*k+13,14*k+14){
        return false
    }
 }
}

A:

I don't have a perfect answer for you but here are my thoughts based on what you said.
Regarding your date function you'll want to.

create an instance of NSDate() which will give you the current date, you'll probably have to format your date using NSDateFormatter so it's easier to work with. Also look into NSDateComponents, they have a .weekNumber property.
you'll want to then match that week number against some sort of stored week number or a switch statement.
your function doesn't necessarily need to take any parameter just make a new NSDate.
If you update your question to be more specific and clear I can maybe provide a better solution and some code.

Regarding checking "without the user doing anything".
If you want to run the function without the user doing anything (like even opening your app). You'll probably want to do this by performing background fetches. Much of the work will be done in the AppDelegate.
In your AppDelegates didFinishLaunchingWithOptions method you'll need to setMinimumBackgroundFetchInterval.
func application(application: UIApplication, didFinishLaunchingWithOptions launchOptions: [NSObject: AnyObject]?) -> Bool {

        // background fetch
        UIApplication.sharedApplication().setMinimumBackgroundFetchInterval(
            UIApplicationBackgroundFetchIntervalMinimum)
}

Then you'll need to add the following method to you AppDelegate which will contain the code you need to perform.
func application(application: UIApplication, performFetchWithCompletionHandler completionHandler: (UIBackgroundFetchResult) -> Void) {
      //... run task once complete call {
           completionHandler(.NewData)
      // }

    }

Ray Wenderlich has a great tutorial on background fetching:
http://www.raywenderlich.com/92428/background-modes-ios-swift-tutorial

