The question is not if Ubuntu supports your hardware or not, it is more if your hardware builder has made any drivers for your hardware to be usable in Linux.

The Radeon HD 6750 is officially supported by ATI's Catalyst drivers and the xserver-xorg-video-ati open source drivers.

The Radeon HD 6750M will work even tough you will find your self with a watermark on the right bottom corner of the screen saying your hardware is not supported. That can be fixed following some simple steps.

The Radeon HD 6490 or the 6490M are not officially supported by ATI's Catalyst drivers but the open source xserver-xorg-video-ati driver should work without a problem.

The xserver-xorg-video-ati open source driver will be installed by default once your card is detected, the performance in not au pair with the closed driver but really big improvements are done with each release so its definitely an option.

You can easily toogle between the open source xserver-xorg-video-ati driver and the closed driver by following these steps.