Extrapolation of a known function

Hello XGBoost Community.

I’m fairly new to ML (I know the basics and dabbled into around with simple problems) and I would like to know if it would be possible to use XGBoost for a time series problem where extrapolation is needed.

When I use a plain Regressor. The extrapolation does not work (which is expected).

Could a known function be used as a guide to help XGBoost extrapolate better?
If so, what should I look into? (I just require some keywords to keep googling further, I’m kinda stuck)