There’s at least 3 different methods you can use to add a full width image in your theme.
This theme includes the code which guarantees your image re-sizes on different sized screens.
The code generates a new widget area before the footer with a background image you can easily change using the customizer. There’s also a default backup image which you can change in the child themes images folder.
The following image shows you exactly what this theme produces before the footer on all pages:
Rather than install all the different types of code yourself, you’ll get access to a default theme with the code already installed.
Here’s the download link for the free theme which includes the preinstalled code: