Charts
As with unary function, charts are
used to graphically display the preferred sectioning
of a function into monotonic pieces.
Charts for some common binary functions follow.
and
charts are both
identical to the 
chart.
Regions where the function is not defined are labelled with 
;
regions where the function is discontinuous are labelled with 
.
The horizontal and vertical arrows point in the direction of increasing g,
for each component of g. For an interval box within a section
the upper bound is given by g(x,y), where (x,y) is the corner
of the box that both arrows point towards. The lower bound is similarly
given by g(x,y), where (x,y) is the corner of the box that both arrows
point away from. This is simply a graphical encoding of the rules
given in the previous subsection.
Since
and 
,
used to aid the determination
of 
, for unary g,
may be used
to aid the determination of , for binary g.
As an example, consider 
,
g(x,y) = xy; since
, which implies
and 
, it follows that
.
| Jeff Tupper | March 1996 |