  We obtain black hole rotating solutions for Horndesky theory (specific
partial case), bumblebee model and Gauss-Bonnet scalar gravity using the
specially improved Newman-Janis algorithm. The shadow profiles for these
metrics were calculated. Applying the limitations from the Event Horizon
Telescope we find the opportunity to constrain model parameters from considered
extended gravity theories. We show that for three considered models two of them
(Horndesky theory and Gauss-Bonnet scalar gravity) weaken the effect of
rotation and bumblebee model enhances it. This conclusion matches the
previously obtained one that extended gravity theories by themselves correct
the effect of rotation in both directions.
