Looking at your video, it does seem that the lecturer is talking about the relationship between functions and their respective gradients. So maybe he should have said "functions and their gradients", or used the singular form in its "generalizing" capacity:
"we've explored the relationship between a function and its gradient"
But this is such a common grammar error that it doesn't even sound strange to me. I think most native speakers of English would not even notice that there was anything wrong with his phrasing unless you challenged them to find the mistake in that specific sentence.
Since the professor's topic is Math and not English Grammar, I think we should excuse him this time. (But yes, you are right.)