affine transformation
a function 
is affine if the function 
is linear. the image of an affine function is called an affine subspace.
unlike a linear transformation, an affine transformation need not preserve the origin of the affine space. thus, every linear transformation is affine, but not every affine transformation is linear. is affine if the function is linear. the image of an affine function is called an affine subspace.[cite:;from @calc_hubbard_2015 definition 1.3.14]