Even though I am using the suggested dimensions for the theme I am using, about 1/3 of my banner image is getting cut off on the right side.
How much of the banner will show will depend on the size of the screen being used to view the page. For example, if you drag the size of your browser window around you will probably see more or less of the image showing.
This is preferable than simply having the image shrink to fit different window sizes - on small screens parts of the image could be very small and hard to see.
Because of this, we recommend using an image that is abstract and doesn't include text - that way, it doesn't matter too much if some of the image gets cut off.
I hope this makes sense, but if you have any further questions at all please don't hesitate to get in touch.