Rough-in Layout

I am new to the world of major plumbing, so please be gentle. I've looked all through this site and others to find a set up similar to that in my basement, but have had no luck. Can anyone help me out with labeling the pipes that I can see? My initial assessment was that there is a toilet drain (black cover), sewer trap (left, level with slab), and a shower drain (on right). Is the 2" pipe (located only 4" behind the black cover) a sink drain or a toilet vent?? I'd rather not combine the toilet tank and the sink (my friends might not think that's too sanitary). Am I going to have to move the 2" pipe, or can it be angled into the wall somehow? Thanks for any help in advance!

I'm going to guess that the thing on the left is a cleanout. You might be able to take out the plug and peek inside to see where things go. The 3" pipe on the right is a mystery -- why 3"? Aren't the as-built plans on file at your local building office? If not, it might be time to call a pro, maybe with a camera.

pull the cap off the one to the right - if there is no trap, it may be set up for the toilet (although attaching a flange will be a fun job), the 2" sticking up is the sink/vent, the one flush with the floor is a check valve/clean out, and the black one is a clean out. I don't think there were plans for a shower.
the check valve and clean out would be concealed (not covered, just concealed) by a vanity.

if there is a trap on the right, then it was meant for a shower, and i'm way off.

Is the floor poured up to the pipe without anything to provide some movement? (bad)

By the way, this is a guess - if it was done with inspections, there should be a plan on file with the city, and a letter that specifies it was only roughed-in.

if the black one is foam, then it was meant for a closet flange. And i have no idea what they were thinking!

Pat, you saved the day. After calling the city and getting shut down, I called the builder. He was no help, either. I saw your post and it provoked me to rethink the bathroom layout. The 3" is for the toilet, the rest on the left is for the sink. There is a drain to the right of the toilet stub, but it was WELL hidden under the concrete. This was no veneer of concrete... It all makes perfect sense, now. I slept well last night! haha
Thanks for your help!

You are welcome.