Graphing Rational Functions
A rational function is any function that is a quotient of polynomials. That is, f(x) is a rational function if f(x)
= p(x)/q(x) where both p(x) and q(x) are polynomials.
For the most part, we will use the calculator for the
graph. However, we will need to
supplement what the calculator gives us by finding a few things.
Intercepts
- x-intercepts
- Set p(x) = 0 and solve for x.
- y-intercepts
- Evaluate f(0)
- Remember,
intercepts are points and thus have two coordinates
Asymptotes
- horizontal
- if
degree(q(x)) > degree(p(x)) then horizontal asymptote y = 0
- if
degree(q(x)) = degree(p(x)) then horizontal asymptote y = (leading
coefficient of p(x))/ (leading coefficient of q(x))
- if
degree(q(x) < degree(p(x)) then no horizontal asymptote
- vertical
- Set q(x) = 0 and solve for x.
- slant
(or oblique)
- will
occur if degree(q(x)) = degree(p(x)) - 1
- we
won't be worrying about these at this point.
Extrema
You may be asked to find relative
maxima or minima. We talked about how to
do these back in chapter 1.