The domain is the set of
all first elements of ordered pairs (xcoordinates).
The range is the set of all
second elements of ordered pairs (ycoordinates).
Domain and range can
be seen clearly from a graph.
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)
yvalues, 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.
Domain:

