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.