Transformation that all points in the plane display into one fixed point in the plane. It is not one-to-one, beacuse all (two) points display on the same point. Domain of this transformation is allpoints in the plane.
Range of this transformation is onr fixed point in the plane.
It is correct? I am not sure. Thanks for help.
If you are saying that your "transformation" is a map ($\theta$ say) from the plane to the plane (so $\theta : \mathbb{R}^{2} \rightarrow \mathbb{R}^{2}$) and it maps every point in the plane to the same single point in the plane (so $\theta ((x,y)) = (a,b)$ where $x$ and $y$ can take any real values but $a$ and $b$ are the same fixed particular values) then the domain (set the map goes from) of this map is $ \mathbb{R}^{2}$, the codomain (the set this map goes to) of this map is $ \mathbb{R}^{2}$ and the range (also called image) of this map is $\{ (a,b) \}$ (notice the range is a set).
The word "transformation" does have a number of different uses in mathematics. Usually it means a map with some particular properties. So you might want to be a bit more precise in your question.