Cleaned up here is a rotation of any function about a generic point.
https://www.desmos.com/calculator/lojbaqqg0q
Drag the center of rotation to move it around, or feel free to change the function y = f(x).
Desmos does get a little slow if you try to rotate say f(x) = tan x about a generic decimal approximated center, but that is understandable, i can only imagine how data intensive that is.
The commands also easily allows to rotate any cartesian equation of the form C(x,y) = 0, such as the equation of a circle x^2 - y^2 - r^2 = 0
Also using similar ideas one can do any plane transformation, such as dilate a line about a point not the origin.