Since you have the hybrid graphics and the Intel controller is present, your active card will be the Intel one. Support for AMD on 16.04 is, well, none. And there are no plans at this point to support AMD cards unfortunately (I also have a hybrid one). There is also no way to install Catalyst onto 16.04 either, and even if you manage to hack it in, it will likely break things.
For now you can do as other have, including myself, and just disable it. This is to preserve a bit of power when running on battery, but mainly (for myself) it's to keep my laptop running cooler.
Here's how I disabled my AMD card (this method is using the default lightdm Display Manager for Unity)
Note: In my examples I use "username". Replace that with your actual user name.
Create a script, place it somewhere in your home folder.
Mine is /home/username/scripts/radeonoff
In this script, put the following
chown username /sys/kernel/debug
chown username /sys/kernel/debug/vgaswitcheroo/switch
echo DIS > /sys/kernel/debug/vgaswitcheroo/switch
echo OFF > /sys/kernel/debug/vgaswitcheroo/switch
echo OFF > /sys/kernel/debug/vgaswitcheroo/switch
Save it and make the file executable either using the properties tab in the gui, or in terminal with chmod 755 radeonoff
Now edit this file as sudo using your fav editor : /etc/lightdm/lightdm.conf
And add this line: session-setup-script = /home/username/scripts/radeonoff
and save.
Now when you reboot, after you login, your radeon card should be disabled.
Verify this in terminal by running sudo cat /sys/kernel/debug/vgaswitcheroo/switch
You should see an output with a line like this 0:DIS: :Off:0000:01:00.0
. And what you're looking for is the line that has "DIS" to also show ":Off".