Q: Low/rough idle, issues accelerating, jerks after slowing down then speeding back up

There could be multiple deficiencies that, added together, create the poor operation. You can look at short and long term fuel trim on a scan tool and make some inferences as to the condition of the fuel injectors. Given the mileage (133,000) and the symptoms, in addition to performing a diagnostic to identify all causes, I would remove all the fuel injectors from the fuel rail and send them out to a lab (Mr. Injector, for instance) for ultrasonic cleaning, measurement, and replacement of the tiny internal filter baskets that get plugged up thence causing poor idle and acceleration. Also, if you have never changed the fuel filter, change that. Don’t waste your money with on car cleaning of fuel injectors or using materials poured into the gas tank. Fuel injectors have internal filters. The filters must be extracted and replaced and so to do the job right, you have to remove the injectors from the vehicle and send them out for service (even shops do not have the appropriate equipment). There are a variety of potential deficiencies in the rest of the fuel, ignition and air induction systems that can also account for what you are reporting. To obtain a comprehensive diagnostic, and evaluation of the running condition of the engine, please request a rough idle diagnostic and the responding certified mechanic will advise you as to the required steps to resolve this. If you have further questions or concerns, do not hesitate to re-contact YourMechanic as we are always here to help you.