This is the invisible ray itself, not the picture it makes. X-rays go through soft material easily and are stopped by harder material like bone or metal, and that difference is what draws the picture. Hospitals use them to look inside a body, and airports use them to look inside luggage. Too much of this energy is not good for the body, so the person running the machine stands behind a wall. When we talk about the energy we usually use the plural: X-rays pass through skin.

The verb behaves normally: X-ray, X-rays, X-raying, X-rayed. You very often meet it in the passive, because the person being checked is what matters: her lungs were X-rayed, all bags are X-rayed. The object is the thing you look inside, not the picture, so you X-ray a hand and you get an X-ray of it. The verb covers the medical use; it is also used of any object, which is how airport notices use it.

This is the flat black-and-white image, the thing you can hold up or open on a screen. Bone comes out white because it stops the rays; soft parts come out dark because the rays go through. It is countable: an X-ray, two X-rays, the X-ray of my wrist. Doctors take an X-ray, and then the X-ray shows something. Say an X-ray of your wrist, not an X-ray for your wrist.

Here the word names the whole visit, not the picture that comes out of it. You go for an X-ray, you have an X-ray, a doctor sends you for an X-ray. The part of the body usually sits in front as a modifier: a chest X-ray, a dental X-ray. It is countable, and it usually takes only a few minutes. If you can replace the word with appointment, this is the meaning you are looking at.