A functor between two preorders is a function $T $ that is monotonic (i.e., $p\le p' $ implies $Tp\le Tp' $).
This is an exercise from Categories for the working mathematician, (number 1.3.3) whose question is not very clear to me. If we have two preorders, isn't the sentence above a consequence of the definition of functor? Suppose we have an arrow $f : p\to p'$ in the preorder $A $; then $Tf $ is by definition an arrow $Tp\to Tp'$, and since $B $ is a preorder we have $Tp\le Tp'$. I don't think this is what the exercise suppose me to do, but I just don't get it. Thanks for any clarify
You've just discovered that "exercises" at least in the very beginnings of category theory tend not to be very exercising: you work through the relevant definitions and bingo!