A function f with domain X and codomain Y is commonly denoted by
In this context, the elements of X are called arguments of f. For each argument x, the corresponding unique y in the codomain is called the function value at x or the image of x under f. It is written as f(x). One says that f associates y to x or maps x to y. This is abbreviated by
y = f(x).
A general function is often denoted by f. If a function is often used, it may be given a special name as, for example, the signum function of a real number x is denoted by sgn(x). The argument is often denoted by the symbol x, but in other contexts may be denoted differently, as well. For example, in physics, the velocity of some body, depending on the time, is denoted v(t). It is common to omit the parentheses around the argument when there is little chance of confusion, thus: sinx; this is known as prefix notation.