I know my old Sapphire HD 6950 couldn't do anything over 1080p @ 60Hz on HDMI.
DVI & DP can run higher desktop resolutions, but most likely only 60Hz.. But they really, REALLY aren't 2K or 4K capable GPU's in any sense. They cannot process 4K video playback. and any game, if it actually runs due to only 1 - 2GB Video memory, looks more like photo slide show set to 5 second intervals.
It's why I picked up a RX 570 at a good $$ as a stop gap until all this Big Navi, Big $$$s, HDMI 2.1 120Hz stuff settles, so I can finally upgrade the GPU to finally see 4K @ 120Hz on my LG OLED.
Not sure what price they're at now. But the RX 570 or 580 does 4K video no worries and if you OC the **bleep** out it can even do MS Flight Sim @ 2K with mix of high - ultra settings and be playable.They really are only a 1080p card..