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 piecewise function.