Once we have a thorough understanding of polynomials we can look
at rational functions that are a quotient of two polynomials.
These rational functions have certain behaviors, and students
are often asked to find their limits, or to graph them. Their
graphs can have different characteristics depending on whether
the numerator function has degree less than, equal to, or
greater than the denominator function. I want to talk about a
very important class of functions called rational functions. A
rational function is one that can be written f of x equals p of
x over q of x where p of x and q of x are polynomials. Now, f of
x is defined for any number of x unless q of x the denominator
equals zero so the domain will be all real numbers except those
that make the denominator zero. And the zeros of a rational
function will be the zeros of the numerator just as long as they
are not also zeros of the denominator, so let's practice using
these definitions in an example. Each of these three is a
rational function, polyno