Someone made the bumblebee open source drivers for intel/nvidia, but I doubt anyone will do it for AMD since its only one series of cards.
That's why I'm hopeful, that like with nVidia, someone or a group will release a PPA to support AMD graphics on 16.04, unless a upgrade to the OS provides this.
After all, it was done for nVidia cards for some time, to have proprietary drivers for Linux, though these still says 'open source' in the Driver Manager. Can the same be pulled off for AMD remains to be seen, yet I have no doubt that someone at least is experimenting. If one can pull this off, that person or group deserves a $10 donation from every AMD graphics user, and we are many strong (though I only have one & nVidia is my favorite).
Thinking back a bit, having nVidia support was an issue, and it required a lot of work, with a lot of assistance by members of this very forum, to get my then new out of the oven GTX 960 to run. And then about another 6-8 months to perfection, just one small line to be uncommented made the Linux Mint logo during boot & shutdown appear. Today it's much easier due to the PPA's, yet at the time it was a feat, and I have to admit, was considering sticking that AMD Radeon 7770 back into the PC & exchanging for an AMD card.
I know that different folks has different experiences, and some are much more well traveled than myself, though until Ubuntu 16.04 came along, one could simply rely on an AMD card for Linux Mint, it was & still is, plug & play.
Have a hunch that used nVidia cards will jump a bit in price on eBay because of 16.04, even some of the famed Fermi models. Yet in this situation, I cannot blame them, it'll be a seller's market for those not wanting to purchase a new card. Though if over $40 (my line in the sand), may as well hop onto a GTX 750 Ti, at least it's GDDR5 & some of the models are 2GB ones, though at 128 bit, that's not going to mean as much as one would think. Especially over a EVGA SC model that's 1GB GDDR5 & uses little power, a few of the GTX 750 line doesn't require a 6 pin power connector, though I prefer one, unless the PC is in a an SFF case. That's where the advantage of not having to plug in a power cable is really noticeable, as many doesn't have one to begin with.
One thing that may bypass this is running 16.04 in a VM, haven't tried it, yet VM software can be freely downloaded & installed. While I prefer VMware because it's an easy to install software & all sorts of rules doesn't have to be created to attach components (one can plug in a new device while the VM is running & can attach), I realize & respect that many will stick with VirtualBox, which has more open source support. On the other hand, all one needs to do join the VMware community & ask questions. I do when needed, regardless of software/hardware used, including non-computer items. There's a forum for most any product imaginable.
I'm going to wait this graphics issue out & see what happens, someone is going to come up with a solution, even if it has to be the open source community.
There's one word that I don't prefer to use, and that's 'impossible'. Though there will be instances of this, say like running modern Linux (even 12.04/14.04 based) on a very early XP box, unless one has one of the non-PAE versions I could once link & it's gone now, though I have several ISO's of it. Still, 12.04 & derivatives will be EOL come April 2017. The day has came, one cannot pick up any old computer by the curb or sticking up from a recycle bin & run the latest Linux titles, though this was the case when I began. Of course, support wasn't as good as now, so it was a good thing that these did run with little trouble.
My recommendation for a distro based off of 14.04 stands for now, unless the user decides to go the non-Ubuntu route, that's where I have little experience & others will be in a better position to say what's supported or not. I prefer the ones based off of Ubuntu because of ease of use. This doesn't imply that's the case for everyone, say if one was raised on BSD, that person won't like Ubuntu after a day, because for starters, BSD is more secure. That's not to imply that Ubuntu & derivatives aren't secure, it's just that BSD goes the extra mile, security comes first & the rest built on top of that base. Yet there's no such thing as a bulletproof OS, though Linux based OS's are as close as it gets.