The following examples
illustrate this:
Example 16 Prove that every rational function is continuous Solution Recall that every rational function f is given by
( )
( )
,
( )
0
( )
p x
f x
q x
=q x
≠
where p and q are polynomial functions The domain of f is all real numbers except
points at which q is zero Since polynomial functions are continuous (Example 14), f is
continuous by (4) of  Theorem 1