Option A : For all x and for all y, if f(x)=f(y) then x=y implies it is a one-to-one function or injection.
Option B : For all y, there exists an x means all elements in the co-domain must be mapped to some element in the domain which implies it is an onto function or surjection .
Option C : For all f(x)=k (k≠0) implies a straight line parallel to x axis i.e.constant.