Section 6.1 The Geometry of Maps from R^2 to R^2.
Please see the attached pdf file.
Let D*=[0,1]x[0,1] and define T on D* by T(u,v)=(-u^2+4u,v). Find the image of D. Is T one-to-one?
This provides an example of finding an image and determining if a transformation is one-to-one.