Transcript Document

2.6 Rational Functions
1. What is the graph of the parent rational
function?
2. How do you find the x intercept of a rational function?
Let y = 0 and solve.
a. What mathematical “tools” will you need to
accomplish this?
The tools you will use depend on what the
polynomial of the numerator is.
You may use factor and/or QF or simple solving.
If the polynomial is of degree greater than 2
you may have to use the Remainder Thm and
the Rational Root Thm ( P/Q) which involves
using long/synthetic division and possibly
evaluating.
3. How do you find the y intercept of a rational
function?
Let x = 0 and evaluate.
a. What mathematical “tools” will you need to
accomplish this?
No tools other than
evaluating need.
4. How do you find the domain for a rational function?
Use will employ the same tools as we did for
finding the x intercept BUT this time we focus
on the DENOMINATOR because we are setting
the denominator equal to zero so we know
which values for x must be limited from the
domain because they would result in a division
by zero error.
5. How do you find the vertical asymptote?
Simply by finding what values make the
denominator equal to zero. This may be a
simple as setting the denominator to 0 and
solving but it may also require us to factor, use
quadratic formula or the Rational Root Thm to
solve
6. How do you find the horizontal asymptote?
Note: While we CANNOT intercept a
VERTICAL asymptote we CAN intercept
(touch/cross) a HORIZONTAL ONE
We have three possible situations:
1. IF the degree of the numerator < than degree of
denominator the horizontal asymptote is : y = 0
2. IF the degree of the numerator = the degree of the
denominator the horizontal asymptote is : the
quotient of the leading coefficients.
3. IF the degree of the numerator > than degree of the
denominator there is no horizontal asymptote
BUT…if the degree of the numerator is
EXACTLY one more than the degree of the
denominator then we have a slant asymptote
which is determined through polynomial
division. We MAY also have a HOLE.
6. Reword the study tips they provided
in this section below.
Reword the “Guidelines for Analyzing
Graphs of Rational Functions” on p.187