Log has the NumericFunction attribute:

When Log has an argument that is a number, constant, or numeric, the result is numeric:

In most cases when NumericQ [expr] gives True , then N [expr] yields an explicit number:

Define f to be a numeric function:

If you have not assigned f to yield numerical values, then NumericQ gives misleading results:

Assign f to evaluate for arguments that are approximate numbers:

Consider the following two function definitions, where one has the NumericFunction attribute:

Define a function that evaluates faster for numeric input than for arbitrary input:

The evaluation of is faster when it is able to recognize that its argument can be treated as numeric:

Define a function that can represent an exact value:

Assign N [f[a]] to give the derivative with respect to a of the solution of an ODE at :

Assign f for approximate numbers:

f[1] does not evaluate but represents a number:

It will work with any precision (within reasonable limits!):

A plot of the function:

Sin has the attribute NumericFunction :

The NumericFunction attribute informs NumericQ that Sin [1] can be converted into a number when using N :

NumericQ can return True without having to evaluate N [Sin [1]]:

Note that NumberQ returns False :

Some of the system symbols that are numeric functions: