Is Avatar: The Last Airbender Anime?

What IS Anime? After binge watching the american produced Avatar: The Last Airbender & Avatar: Legend of Korra, the question seems more complicated. The general consensus in the west is that anime is a product of Japanese culture, and TRUE anime can only come from Japan. But would it blow your mind that in Japan, ANYTHING animated is anime (including Family Guy)?! So what defines anime - visual and tonal style? Geographic borders? Is there a reason to keep the definition of anime limited?