Cycle of a dominant morphism $f:V\rightarrow \mathbb P^1$

Question

I am referring too Example 1.5.1. In "intersection theory" by Fulton. I am given a dominant morphism $f:V\rightarrow \mathbb P^1$ and we define for a rational function $r$ $[\mathrm{div} (r)] =\sum \mathrm{ord} _W(r) [W] $, where we sum over all codimension 1 varieties. Now if we denote the rational function given by $f$ also by $f$. Why is it that we have $[\mathrm{div} (f)] =[f^{-1}(0)]-[f^{-1}(\infty)]$?