Opposite of a function being bijective? A function is bijective if it is both surjective and injective. Is there a term for when a function is both not surjective and not injective?
As far as I know, there isn't.  The concept of a "non-surjective and non-injective function" just doesn't generally arise often enough to need a special term.
Of course not. This would be a useless notion (so there is no need for such terminology). Most functions are not surjective or injective (in the sense that if you take a "random" one, then you cannot expect it to be surjective or injective), mind you. We are mostly interested in the special class of mappings called injections and surjections, and for this reason the terminology "injective" and "surjetive" is useful.