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=√x^{2}, 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 piecewise function.