A hybrid graph, in mathematics, is a graph with multiple rules for x. It usually results in an irregularly-shaped graph, sometimes with an open or closed circle, both indicating discontinuity.
A typical hybrid graph, and its corresponding rule, would look like:
_
| x if x<-1
f(x)=-| 1 if -1<x<1
|_-x if x>1
|
o--|--o
|
|
-1 | 1
-----------o--|--o----------
/ | \
/ | \
/ | \
/ | \
/ | \
The graph can be differentiated at all points except those where there is discontinuity. For this hybrid:
- d/dx=1 if x<-1
- d/dx=0 if -1<x<1
- d/dx=-1 if x>1
Which means that the following is a graph of d/dx for this particular hybrid:
|
-----------o |1
|
|
-1 | 1
-----------o=====o----------
|
|
|
-1| o----------
|
Examples of other hybrid functions include the absolute value, or modulus, function (where y=√x2, xεR) or the greatest integer function.
Hybrids commonly have no set rule, but are found on statistical graphs, such as stock exchange graphs.
See also peacewise function. | 
