I think that UPDATE() is incorrect answer.

The question was:

"Within a trigger, how can you tell if a value has altered on a specific column? "

The explanations for the UPDATE() in BOL are:

"Returns a Boolean value that indicates whether an INSERT or UPDATE attempt was made on a specified column of a table or view. "

First, as other posters pointed here, the attempt does not mean the update was successful.

Second: the question is asking about the value being altered, not about the value being inserted.

So you can not tell by this function if the value was altered, or new value inserted or just attempts were made.