Page 134 - Concise Encyclopedia of Robotics

Function
The drawing shows an example of a function as a mapping between two
sets. Not all of the elements in the left-hand set (a few of which are shown
by black dots) necessarily have counterparts in the right-hand set.Similarly,
not all of the elements in the right-hand set (a few of which are shown by
white dots) necessarily have counterparts in the left-hand set. If the map-
ping is to qualify as a function,it is possible for more than one element from
the left-hand set to be mapped onto a single element in the right-hand
set, but no element in the left-hand set can have more than one mate in
the right-hand set. A function never maps a single element into more
than one counterpart.
Set mapped from

Set mapped into
Function

As shown in the illustration, the set of all elements on the left that have
mates in the right is called the domain of the function. The range of the
function is the set of all elements on the right with corresponding elements
in the set on the left.
See also DOMAIN OF FUNCTION and RANGE OF FUNCTION.
In logic, a function, more specifically called a logic function, is an
operation that takes one or more input variables, such as X,Y, and Z, and
generates a specific output for each combination of inputs. Logic func-
tions are generally simpler than mathematical ones, because the input
variables can only have two values: 0 (false) or 1 (true).

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