Are pixels rendered outside of the camera view?

i understand frustum culling prevents sprite objects outside the camera view from being rendered, however if the background is one large sprite, is the entire sprite rendered even the pixels outside the camera view? If so, it’d be better to break up the large sprite into smaller sprites to utilize frustum culling, right? Or maybe I’m over complicating it, is there such thing as rendering a pixel not seen on the camera? Because if there isn’t, then its better to just keep one large image to keep the object count low. Sorry if this is a basic question, ive never had the entire background on one sprite.

I guess that you are building 2D content.

I’m not sure for 2D but for 3D content the culling will only “hide” the objects that are fully out of the camera view (or fully hidden behind other objects for occlusion culling). If even a small part of the object is visible then the full object will be drawn. So in short no, there is no pixel culling.

As of wether you should have many small objects and use culling or just big objects with fewer triangles (and less culling), this is a difficult question, and I don’t think there is a generic answer to it. If you have optimization issues have a look at this.
And if you don’t then don’t worry to much about it, optimization is very tricky ^^.