Preserving inclusions, and unions.

Let f:A->B. Let $\displaystyle A_0$$\displaystyle \subset$A and $\displaystyle B_0$$\displaystyle \subset$B. Show that f preserves inclusion and unions only:

question: f($\displaystyle A_0$$\displaystyle \cup$$\displaystyle A_1$) =f($\displaystyle A_0$)$\displaystyle \cup$f($\displaystyle A_1$).

I'm not very good with the latex code and I just want to mention that I'm not sure why some things besides the 0 and the 1 look like subscripts. hopefully its not too confusing.