Invariant affine subspaces: It's possible that $\dim(f(V))\neq\dim(V)$?

Question

I'm studying geometry right now. I saw that an affine subspace $V$ is invariant under $\ f\ $ if $\ f(V)\subset V$. After reading that, I wondered this:

Is it possible that $\dim(f(V))\neq\dim(V)$?

That is: Could be $V=P+\langle\vec{v_1},\vec{v_2}\rangle$ an invariant affine subspace and $f(V)=Q+\langle\vec{v_1}\rangle$? Or in other words, an invariant plane can be converted under $f$ in a line?

Answer 1

Yes this is possible.

An example is an affine projection of a space (whatever its dimension) on a line.