What is the lexical class of the word 'worth' when used in a sentence like "Is this apple worth $3?"

The question "Not worth the paper it's printed on" - wrong meaning? got me thinking about what part of speech, or lexical class, the word 'worth' takes?

A comment in Which is correct: "is it worth it?" or "does it worth it?" advises to treat 'worth' as an adjective, but I'm not sure that's right. 'Worthy' is an adjective, but that's not the same as 'worth'.

In the title question you could replace 'worth' with the phrase 'of comparable value to'; what part of speech would that phrase be considered? Are the word and the phrase in the same lexical class?

Edit:

Just to throw another option out, after a stimulating discourse under the answer provided by @Henry:

Wiktionary mentions that used in the context of this question, 'worth' is considered an adjective, but it also notes that

The modern adjectival senses of worth compare two noun phrases, prompting some sources to classify the word as a preposition. Most, however, list it an adjective, some with notes like "governing a noun with prepositional force."

It also notes that

Joan Maling (1983) shows that worth is best analyzed as a preposition rather than an adjective.

If viewed as a preposition, then it is easy to replace 'worth' with another preposition of somewhat equal meaning, such as "Is this apple about $3", "Is this apple under $3", or "Is this apple over $3".

Adjective, infinitive, or preposition? ...or is this a rare case of an old language usage that straddles multiple lexical classes in modern language?

Solution 1:

The Cambridge Grammar of the English Language (CGEL) has a lot to say about worth. It is a little like an adjective and a little like a preposition. I will argue both sides, for your entertainment.

Worth is clearly a preposition, because:

It requires a noun phrase after it. This is what prepositions are known for. Many adjectives take preposition phrases (afraid of bees, tantamount to surrender) or clauses (mad that you didn’t tell her). Almost none take noun phrases.
The vast majority of adjectives can be used attributively—that is, in front of a noun they modify. That is what adjectives are known for. But a worth $5 vanilla shake is wrong.
Consulting my adversary’s points below, I see nothing but desperate gibbering really. “Set off by a comma”? “Fronting”? How about basic syntactic properties?

Worth is clearly an adjective, because:

There is a simple test that distinguishes adjectives from prepositions extremely well. Adjective phrases set off by a comma at the beginning of a sentence always modify the subject. Preposition phrases sometimes don’t.

From the beginning, I liked the book. (ok - preposition phrase)

Consistently excellent, I liked the book. (wrong - adjective phrase must modify subject)

Worth every penny, I liked the book. (wrong!!)
Prepositions are often “fronted” in questions and certain other clauses. Worth isn’t.

From what country did the U.S. purchase the Louisiana Territory in 1803? (ok)

Worth what was the Louisiana Territory at that time? (wrong)

They will want the amount for which they could have sold it last May. (ok)

They will want the amount worth which it was last May. (wrong)
Consulting my adversary’s points above, I see a disappointing failure to go any deeper than the surface—and a few dirty rhetorical tricks. He knows very well that a worth $5 vanilla shake is wrong for the same reason an afraid of bees child and a willing to chip in uncle are wrong: you just can’t put phrases with post-head dependents in that position. And plenty of adjectives can’t be used attributively at all: an afraid child is wrong too.

CGEL calls worth an adjective, but ultimately I think Cerberus is right. The patterns grammarians detect in language are not inviolable laws. Not every word fits cleanly into the categories.