A question for the techno-savvy re: high precision AF points

I understand that on many cameras there are high precision AF points that can be addressed providing one is using an f/2.8 or faster lens.

My question is what happens to the availability of these high precision points when a 1.4xTC is introduced? I know the lens then effectively becomes an f/4, but does the camera now react to that or is the fact that the native lens is f/2.8 all that matters?

The important point is the relative size of the aperture as viewed from the sensor, so I'm afraid that means that using the extender with an f/2.8 lens will switch off the high precision points.

Certain 1D camera models do allow high precision (not cross type) at f/4 for certain lenses, so you may get away with it on such a camera. But you have to consult the specific user's manual for the model in question to see that.

Generally, the answer above is correct.

Thanks a lot, guys. I suspected as much but it's a question I've had in my mind for a long time.