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3.2.24 tex2html_wrap_inline34501 Charts

As with unary function, tex2html_wrap_inline34501 charts are used to graphically display the preferred sectioning of a function into monotonic pieces. Charts for some common binary functions follow.

figure14393

The tex2html_wrap_inline35329 and tex2html_wrap_inline35331 charts are both identical to the tex2html_wrap_inline35333 chart. Regions where the function is not defined are labelled with tex2html_wrap_inline32389 ; regions where the function is discontinuous are labelled with tex2html_wrap_inline32461 . 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

math16299

the relationship, between tex2html_wrap_inline34555 and tex2html_wrap_inline34221 , used to aid the determination of tex2html_wrap_inline34489 , for unary g, may be used to aid the determination of tex2html_wrap_inline34489 , for binary g. As an example, consider tex2html_wrap_inline35371 , g(x,y) = xy; since

math16309

and tex2html_wrap_inline35379 , which implies tex2html_wrap_inline35381 and tex2html_wrap_inline35383 , it follows that

math16313

math16317

From this, it follows that tex2html_wrap_inline35389 .


next up previous notation contents
Next: 3.2.25 Examples with a Binary Up: 3.2 Constant Interval Arithmetic Previous: 3.2.23 Binary Functions
Jeff TupperMarch 1996