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近づける is a transitive verb.
But there is a case in which 近づける is used without an object as the following sentence quoted from another answer.
When there is no explicit object given for 近づける, do we have to assume the object is actually the same as the subject?
It means Y can be rewritten as
近づける is transitive, and its intransitive counterpart is 近づく. The te-form of 近づける is 近づけ(-て), while the te-form of 近づく is 近づい(-て).
Sentence Y uses this intransitive version, in its te-form. No wonder it doesn't require a direct object.
Sentence Z hardly makes sense to me, but compare the following two sentences, which are very similar in meaning.
