Which clauses in these sentences are restrictive?
1. the girl who owns a red car is the one we are looking for.
2. the dog that ate my homework is called henry.
3. i'm saving the muffins that have cherries for my sister.
4. the smile that she gave them was beautiful.

The following are the restrictive clauses in these sentences, as they have an identifying function. Without these clauses the sentences still read as gramatically correct, but do not necessarily communicate all the important information.
 1. 'who owns a red car'.
 2. 'that ate my homework'.
 3. 'that have cherries'.
 4. 'that she gave them'.

In this sentence, hard is the adverb because it is modifying the verb.