Acar is rounding a circular curve of radius r on a banked turn. as the drawing indicates, there are two forces acting on the car, its weight mg and the normal force fn exerted on it by the road. which force, or force component, provides the centripetal force that keeps the car moving on the circular path?

The centripetal force is provided by the x component of the Normal Force.

Explanation:

The centripetal force is a force that makes something to follow a cicular trayectory, this force is always oriented to the center of the circunferency-

So you can see in the image that i attached there is only two forces actting on the car, the normal force and the weigth, and as you can see the y component of the normal force cancels with the weigth, but the x component of the normal force (as it has nothing to cancel with) makes the car follow the circular trayectory so this is the centripetal force.