My wife and I recently purchased a 2013 Mazda 3 s, from a local used car dealer.
We only got one key. Key only, no fob.......

Here is our issue. I had it back to the dealer to check the right front door lock.
I told service that I have to lock and unlock each door individually.
That when I lock or unlock the driver's door, nothing happens. Only the driver's door opens.

The service department told me that this is the way this Mazda is because it is the base model.

Since this is our first Mazda, w needed a second vehicle, good shape, drives great, but, I need another key....

So. Can anybody tell me if what service at the dealer is correct or. should opening the driver's door unlock the rest of the Mazda and is there a problem with the locking system.
Also. would anyone know if there is a key fob that would work with the base model or would I need one?

Getting just a key with a chip is no big deal.

We just need another key and one that works.

Thanks in advance...