Mazda Repair Questions? Ask Mechanics for Answers ASAP
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Sounds like you may have a few different concern going on here.
Inspect to make sure the check engine light is not on and no fault codes are stored in the computer.
With the engine running, look/listen under the hood for any sign of a vacuum leak. Inspect the air hose between the air filter and engine throttle body for cracks.
If the engine runs smooth on accelerating from a stop, the fuel, and ignition system should be good. If it lacks power and runs rough during acceleration, you should replace the ignition coils, plugs and wires.
If the engine has a idle concern at stop light, you will need to remove and clean the throttle plate, throttle body and idle speed control valve. If idle is still low/high or stalls, replace the IAC valve. (#2 and #9 in diagram.)
If the engine has a vibration at idle, I suspect a broken engine/trany mount. You will need to remove and inspect all mounts for wear/damage and replace as necessary.
Please let me know if you have any additional questions by hitting the reply button. ThanksDrew