92 prelude fuel pump relay

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I just took my car to the shop for an inspection and the car failed the emissions test, so the shop told me that a tune up would probably enable me to pass the emissions test. After the tune-up was done they told me I passed the emissions test. I drove the car off and started noticing that the car would buck/lose power at various points over the next several days--generally when the car heated up it would get worse. I took it back to the shop and they figured out that the fuel pump relay was bad. This fixed the problem; however, I'm wondering if this was really the cause of the emissions test failure as well and if I would have never needed the tune up had they figured it was the relay in the first place?? Anyone have any thoughts? thanks.