I was wondering if you are able to play games that have DirectX 10 or lower with DirectX 11? I don't think this is the correct area to post this but, let me know if it is.
All video cards are fully backwards compatible with older versions of the APIs that they support, but never forwards compatible.
This means that any graphics card that supports DirectX 11.0 will support all previous versions of DirectX including 9.0c, 10.0, and 10.1. They will not however support DirectX 11.1.
The same is true for OpenGL. The new Radeon HD 7790 supports up to OpenGL 4.3, but 77xx-79xx support only up to 4.2, while 73xx-76xx support only up to OpenGL 4.1