Is it acceptable in an academic interview to pretend like you derived something, or to explaining where it is from
I really don't think the interviewer cares one way or another whether you've seen the problem before.  She just wants to know if you can solve it, and to hear how you go about it.

In the video, she does say "the function that I'm going to write down, you've probably not seen before"; but I interpret that as just a way to reassure the student that the problem should be possible to solve whether she has seen the function before or not.  It's so the student doesn't panic or get stuck trying to remember the function, rather than actually trying to solve the problem.

So I don't think there is any point in either pretending the problem is new to you, or in announcing that it's familiar.  Neither will significantly help or hurt you in itself.  If you know how to solve the problem, solve it and move on.

On the other hand, it probably wouldn't be helpful to just draw the graph from memory and say "here it is, done".  The interviewer is almost certainly more interested in having you demonstrate that you understand the concepts and methods used to solve the problem, than in seeing if you know the solution.  So you would be wise to work through the problem methodically, explaining what you are doing and how you know to do it.