A function `f`:A→X is said to be *onto* if it maps some element of the domain A onto every element of the range X. That is, its image is equal to its range.
In symbols, "`f`[A]=X", or

∀ `x` in X
∃ `a` in A
s.t. `f(a)`=`x`.

For example, the function `f(x,y)` = `x`^{2} - `y`^{2} is onto **R**,
but `f(x,y)`=`x`^{2}+`y`^{2} is not (it takes on only non-negative values).

A function which is *onto* is also said to be surjective.