The following gallery of graphs demonstrate the care GrafEq
takes while producing graphs. Interested GrafEq
users can generate portions of the graphs at any resolution using GrafEq.
We invite users of other graphing packages to try some of the graphs as well...



Spike
This demonstrates a shortcoming of any simple sampling method.
The abrupt vertical asymptote in the graph is missed by many graphing programs,
although zooming into the asymptote will reveal it. (But you have
to know it is there first!)



Circular Spike
Similar to Spike, but more convincing for some,
since there is a natural view which causes problems for many graphing techniques.
Zooming into an “asymptote” will cause other details to leave the view.


Densely (un)Defined Function
A graph of the function x^{x}; although the graph does not
immediately appear to be a function, closer examination
will reveal its true nature. Most graphing programs do not define the exponential function for negative bases.



Solid Disc
This graph demonstrates how to convert an implicit relation
into an equivalent implicit equation.
Common belief that “equation = linelike,
inequality = arealike” is refuted by this graph.
Many graphing programs base their techniques on this erroneous common belief.


Partial Inequality
Correct graphs of inequalities involving partial functions are likely only if partial functions
are carefully handled. A graph of the area beneath the square root is shown here.



Infinite Frequency
A common graph, of interest to students of introductory calculus.
Not as difficult to handle as Spike, since its change in frequency
is smooth—yet many graphing programs still generate misleading graphs for
this function.


Smooth Step
Here is a graph of a continuous function that approximates a step function.
Programs that can draw discontinuous functions might misclassify (and
thereby misdraw) this sort of function.



Wave
The function (sinx)/x can be problematic for some graphing techniques for x near zero.
A GrafEq graph of y=(sinx)/x is shown.

Any other troublesome graphs out there? We would be glad to try out
and put up here, even if
GrafEq
graphs them incorrectly.
There are graphs that
GrafEq
has trouble with—can you find them?
