A
function
is a correspondence (or rule) that assigns to each member
of some set called the
domain
exactly one member of a set called the
range
.
Definition 2
.
Let the domain and the range of the function be the sets of real numbers.
The
graph of the function
is the set of all ordered pairs
(x, f(x))
in the plane for all members
x
from the domain.
To graph a function, we find ordered pairs (x, f(x)), plot them and connect the points.
x
f(x)
-5
-10
-2.5
-5
2.5
5
5
10
If a vertical line drawn anywhere on the graph intersects the curve in more than one point,
then there will be more than one number in the range corresponding to a member of the domain.
The graph is not the graph of a function.
The Vertical Line Test
If it is possible for a vertical line to intersect a graph more than once the graph is not the graph of
a function.