Greatest Integer Functions, Sgn Functions and Piecewise Defined Functions

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Greatest Integer Functions and Sgn Functions involve discontinuities that can sometimes be difficult to analyse.  Simple functions such as

 

y = gint(x)

 

are easy to interpret and discontinuities will be correctly shown.

 

fxgclip0219

 

Due to the graph tool's ability to graph functions of arbitrary complexity it is possible to construct functions that confuse the graph tool's analysis routines and have the discontinuities incorrectly shown.