How to if determine Finite State Automata with union is deterministic

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I've been looking at this NFA problem for a while now (L = {b^m a^k : m ≥ 0, k ≥ 0}U{a^n : n ≥ 1) and I'm just a little confused about how the union interacts with the FSA and when a string would be accepted. This is the model I made to represent the language but I'm not sure if it's correct.

FSA diagram

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