SOLUTION: I need to know how to find the asymptotes and then graph????
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Question 198680This question is from textbook
: I need to know how to find the asymptotes and then graph????
This question is from textbook
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
Horizontal Asymptotes
A rational function has at most 1 horizontal or oblique asymptote.
Compare the degree of the numerator polynomial (
) to the degree of the denominator polynomial (
)
If 
then there is a horizontal asymptote at the line 
If 
then there is a horizontal asymptote at the line 
where 
is the lead coefficient on the numerator polynomial and 
is the lead coefficient on the denominator polynomial.
If 
then there is an oblique asymptote defined by 
where is the lead coefficient on the numerator polynomial and is the lead coefficient on the denominator polynomial.
If 
then there is no horizontal or oblique asymptote, though there may be higher order curves to which the function is asymptotic.
Vertical Asymptotes
A rational function has a vertical asymptote at 
for every factor 
of the denominator polynomial that does not have a corresponding factor in the numerator. For example:
 = \frac{x^2 - 5x + 6}{x^3 - 3x^2 + 2x} = \frac{(x - 2)(x - 3)}{x(x - 2)(x - 1)})
has vertical asymptotes at 
and 
but not at 
John
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