Example 3: Graphical Rules

Click here to open an associated Mathcad worksheet:

A graph can also represent a rule. Here is a graph for a rule  h  (in fact, a function  h ) which assigns the same values (black, red, blue) to the temperatures  w  = 10, 20, and 30 as does the function  g  represented by the table in Example 2. This function, however, is defined for all temperatures  w  > 0.

The rule  h  has a larger domain than the rule  g . Since  h  and  g  agree on their common domain, however, we say that  h  is an extension of  g .