1. He is not as old as me.

(Is 'as' before 'me' a preposition or a conjunction?)

2. He is not as old as I.
3. He is not as old as I am.
(Is 'as' before 'I' or 'I am' a conjunction?)

#1 is grammatically incorrect.

The word "as" here is a subordinating conjunction, and there are a few missing (but understood) words here.
http://grammar.ccc.commnet.edu/grammar/conjunctions.htm#subordinating_conjunctions

#3 is the entire correct sentence. You can see "as" in its conjunction position there, joining the independent with the dependent clause.

#2 is the grammatically correct, shortened form of #3.

This also applies -- http://grammar.ccc.commnet.edu/grammar/conjunctions.htm#correlative_conjunctions -- since there is the "...as...as..." combination going on in those sentences.

In both sentences 1 and 2, the word "as" is functioning as a conjunction.

In sentence 1, the word "as" is used to compare the age of "he" with the age of "me." It introduces a clause ("as old as me") that functions as the object of the verb "is."

In sentence 2, the word "as" is also used to compare the age of "he" with the age of "I." However, in this sentence, "I" is used as a subject pronoun in the clause "as old as I."

Sentence 3, "He is not as old as I am," includes the full form of the subject pronoun "I" and retains the verb "am" after "I." In this case, the word "as" is a conjunction that connects the clauses "as old as I" and "am."

In the given sentences, the word 'as' is functioning as a conjunction.

1. In the sentence "He is not as old as me," the word 'as' is a conjunction. It is used to introduce a subordinate clause ("as old as me"), which is comparing the age of two people.

2. In the sentence "He is not as old as I," the word 'as' is again a conjunction. It introduces a subordinate clause ("as old as I"), which is comparing the age of two people. In this case, 'I' is used in the nominative form because it acts as the subject in the subordinate clause.

3. In the sentence "He is not as old as I am," the word 'as' functions as a conjunction. It introduces a subordinate clause ("as old as I am"), which compares the age of two people. Here, 'I am' is used in the nominative form because it acts as the subject in the subordinate clause.

To determine whether 'as' is acting as a preposition or a conjunction, you can examine its role in the sentence. If it introduces a subordinate clause that contains a subject and verb, it is functioning as a conjunction. If 'as' is followed by a pronoun in the objective form (like 'me'), it indicates a comparison and functions as a conjunction. On the other hand, if 'as' is followed by a pronoun in the nominative form (like 'I') or a subject-verb construction (like 'I am'), it functions as a conjunction.