I took the ESL certification test and I was wondering: what is it called when you add 'im' to 'possible'?
Adding a prefix to a word is called prefixation, as Kosmonaut pointed out.
The answer is that in- becomes im- before words starting with 'p', 'b', or 'm' (as in impatient, imbalance, immature, etc.), because of a process of euphonic sound change known in Sanskrit as sandhi (pron. "sun-thee"), a term that appears to have some currency among general linguists as well. Specifically, it's a form of internal sandhi (the kind that would be called parasavarṇa sandhi in Sanskrit, but I don't know the equivalent term in English linguistics).
To add a prefix to a word is called prefixation, as Kosmonaut points out.
To add any kind of affix (prefix, suffix, infix, circumfix) to a word is called affixation.
To form a new word out of another word by means of affixation is called derivation or sometimes agglutination.
The semantic process (effect on the meaning) is called "negation" or "privation".