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Question 1089798: Analyze the graph of the function. R(x)= x^2+6x-27 /x-9
a) What is the domain of R(x)?
b) What is the equation of the vertical asymptote(s) of R(x)? x=
c) What is the equation of the horizontal or oblique asymptote of R(x)? y=
Answer by MathLover1(20849)   (Show Source):
You can put this solution on YOUR website! 
vertical asymptote:
Vertical Asymptotes of  :
An asymptote is a line that the curve approaches but does not cross. 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.
if  ->
Vertical asymptote is
The location of the  asymptote is determined by looking at the degrees 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  or slant asymptote.
in your case  and  , so which means there is asymptote
To find the equation of the asymptote, perform long division (synthetic if it will work) by dividing the denominator into the numerator.
-------x+15
(x - 9) |x^2 + 6 x - 27
---------x^2-9x
----------0+15x
-------------15x-27
-------------15x-135
----------------0+108
is asymptotic to 
Oblique asymptote: 
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