A bijective function, also known as a bijection, is a type of function between two sets, where each element in the domain (input) set is paired with exactly one element in the codomain (output) set, and vice versa. In other words, a bijective function establishes a one-to-one correspondence between the elements of the domain and the elements of the codomain.

Formally, a function f:A→Bf:A→B is bijective if and only if:

1. Every element in set BB is mapped to by exactly one element in set AA, i.e., for every yy in BB, there exists a unique xx in AA such that f(x)=yf(x)=y.
2. Every element in set AA is mapped to by exactly one element in set BB, i.e., for every xx in AA, there exists a unique yy in BB such that f(x)=yf(x)=y.

In simpler terms, a bijective function is both injective (or one-to-one) and surjective (or onto). It means that each element in the codomain is paired with exactly one element in the domain, and there are no "extra" elements left in either set without a corresponding match in the other set.

Graphically, a bijective function can be represented by a plot where each input value has a unique corresponding output value, and there are no horizontal or vertical line tests that intersect the graph at more than one point.