Is "this" an adjective or determiner if you are doing a syntax tree diagram branching out from a NP?

Question

I will surely leave this job without a penny in my pocket.

Is "without" a preposition?

Answer 1

Yes, "this" is a pronominal adjective or a determiner.

And yes, "without" is a preposition.

=)

Answer 2

yes it is a preposition