Question 984292: find the vertical, horizonal, and oblique asymptotes, if any , for the following rational equation
t(x)=x^3/x^4-81
Answer by MathLover1(20849)   (Show Source):
You can put this solution on YOUR website! 
recall:
if you have  , then:
The domain of a rational function is all real values except where the denominator,  .
The roots, zeros, solutions, x-intercepts of the rational function will be the places where  . That is, completely ignore the denominator. Whatever makes the numerator zero will be the roots of the rational function, just like they were the roots of the polynomial function earlier.
If you can write it in factored form, then you can tell whether it will cross or touch the x-axis at each x-intercept by whether the multiplicity on the factor is odd or even.
The equations of the vertical asymptotes can be found by finding the roots of  . Completely ignore the numerator when looking for vertical asymptotes, only the denominator matters.
The location of the horizontal asymptote is determined by looking at the  of the numerator ( ) and denominator ( ).
If  , the x-axis,  is the horizontal asymptote.
If  , then  is the horizontal asymptote. That is, the ratio of the leading coefficients.
If  , there is  horizontal asymptote.
However, if  , there is an oblique or slant asymptote.
Horizontal asymptote:
the of the numerator and denominator are
 ) and denominator (
 , and the x-axis, is the horizontal asymptote
 as  or 
Vertical asymptote:
find the roots of 
 or  (two double solutions)
so
 or  as  or 
since => , there is  oblique or slant asymptote
|
|
|
