I have an HD 7970 and a 4k tv (Sony XBR-65X850C) but for some reason it isn't displaying 4k. I'm using the display port of the Graphics Card (not the old hdmi1.2 port).
After l did some research it seems as though I should be able to display 4k on the TV at 30Hz https://docs.sony.com/release//specs/XBR65X850C_mksp.pdf
My computer claims that the TV's maximum supported resolution is 1080p (which I know isn't true).
If I do use the old hdmi1.2 port I can get 4k at 24Hz but it's unbearable.