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Eric, if you'll look in our Liberry you'll find a thread for Lumber Notching and Boring Guides. Either of the links in there will be helpful in diagnosing the problem you've got
The maximum hole you can bore in a nominal 2x10 floor joist is 3 inches. The minimum wood that must remain from the top or bottom of the joist to a bored hole is 2 inches.
If you meet those guidelines, your joist is considered whole. If you don't, you would need to correct the deficiency.
Viewing your photo, it's gonna be difficult to correct what you've got even with the correct method of "headering off" the deficient joist as would be done in new construction. There's always a way, but the only way plumbers know is to chop away whatever wood is in the way of their pipes. And they're generally not sufficiently careful to cut a hole in the joist rather than just notching it or chopping it off completely.
Without being able to see the rest of your floor and plumbing there's not much I could suggest. If you think you meet the guidelines, or think you're close enough for your comfort level, you can, of course, move on with what you've got.
My opinion; worth price charged.
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