onto

(of a function) Assuming each of the values in its codomain; having its range equal to its codomain.

“Considered as a function on the real numbers, the exponential function is not onto.”

Upon; on top of.

“My cat just jumped onto the keyboard.”

Aware of.

“The thought-police were onto my plans of world domination.”

Being an onto function with a codomain of (see below).

“The exponential function maps the set of real numbers onto the set of positive real numbers.”