Graphing, Domain and Range of Functions
Topic Index | Algebra2/Trig Index | Regents Exam Prep Center

The domain is the set of all first elements of ordered pairs (x-coordinates).
The range is the set of all second elements of ordered pairs (y-coordinates).

Domain and range can be seen clearly from a graph.

Example 1: Example 2:

Domain: {1, 3, 4, 6}
Range:  {-2, 2, 5}

Domain: (all real numbers)


The two examples shown above are functions.  But, as we know, not all graphs are functions. 

The graph at the left is: 

Since the graph FAILS the Vertical Line Test, this relation is not a function.

If we restrict the graph to only the "positive" (or we could have chosen negative) y-values, the graph will be a function:
                             (graph below)


In a similar fashion, we can also restrict domains to ensure that graphs are functions.

The graph at the left is:  

If the domain for this graph is listed as "all Real numbers", this relation is NOT a function.  At first glance this graph appears to pass the Vertical Line Test, but it is actually undefined at x = -1.

If we restrict the domain to be "all Real numbers excluding -1", our relation will be a function.