Yes. Click on the drive, and then from the File menu, pull down to Get Info. It should say Format: Mac OS Extended (Journaled) if you paid extra for a Mac formatted drive. But it takes about 1 minute to format the drive properly if it says FAT32, or Windows File System, using Apple's Disk Utility, in the Utilities folder, in your Applications folder.

Any drive that works with your OS will "support" this drive--both drives should just show up on the desktop on a Mac, or under My Computer/This Computer on a PC.

First, format the drive for a Mac, using Disk Utility, in your Utilities folder, in the Applications folder.
To format the drive as a Mac drive, so you can boot from it, in a pinch, do this:
1. Plug the drive in to your Mac's USB port. It should have come with a single USB 3.0 plug, which provides both power and data to the drive.
2. Click Go:Utilities from the menu bar, at the top of your screen.
3. Double-click Disk Utility
4. Click the name of your Seagate Backup Plus in the left-hand column, to select it.
5. Click the "Partition" tab over in the right part of the window. Choose 1 partition from the drop-down, (under Partition Layout) and then click "Options" at the bottom, and select GUID, at the top. The other two choices are for older macs, or for a Windows format drive.
6. Under Partition Information, call your drive something like Jill's Backup HD or something you can recognize, and for Format, choose "Mac OS Extended (Journaled.) The other formats can be problematic unless you're pretty knowledgeable, and have special requirements.
7. Now, click Apply. Wait a minute, and your newly formatted drive will appear over on the right of your desktop.

Now that you've formatted your drive as a Mac drive, do this:

Google SuperDuper, from Shirt Pocket Software, and buy it. Reason: It's better than Time Machine! Time Machine runs once an hour all day long, and can slow you down when you're trying to do some work. Super Duper makes a bootable backup, and you can easily program it to run once a day.

I use it myself like this--click the Apple, pull down to System Preferences, open the Energy Saver control panel. Click the Schedule button on the bottom right, and set your Mac to wake up or turn on at 2:00AM, or whatever time is convenient for you. Then launch Super Duper, and make a full backup of your drive to the portable. A full backup can take a couple of hours. Next, click the Options button on SuperDuper, and check the box to "Repair Permissions" before you run a backup, and switch "Erase, then Backup" to "Smart Update" which mimics the first choice, but only takes about 20 minutes a day. Check out the options, and you can have your Mac turn off when Super Duper finishes, or just go to sleep, or actually restart from your backup drive.
Sounds über geeky, but it's really not that hard, and Apple and Shirt Pocket software will be happy to help you. Or I will! Takes me about 10 minutes to do this stuff. And you only pay for SuperDuper once, not over and over like other disk utilities. I've had it on my Mac for about 10 years.

Just unplug both ends of the USB cable, then plug it back in. Oxidation happens. Cycling the plugs scrapes it off.