SOLUTION: 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

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:

RELATED QUESTIONS
analyze the graph of the function: R(x)= x^4+x^+10/x^2-100 What is the domain of R(x)... (answered by edjones)

Using the seven steps, analyze the graph of the following function to get domain,... (answered by lynnlo)

I am struggling with this problem... any help will be greatly appreciated! Analyze the (answered by josgarithmetic)

analyze and graph of the function f(x)= x^2-2x-3/x+17 a) what is the domain of f(x)... (answered by brysca)

Analyze the graph of the function. R(x)= x^4 + x^2 +10 /... (answered by nyc_function)

What is the equation of the slant asymptote for R(x) = x^2-6x+8/x-4? a. R(x) = x � 2 b. (answered by Edwin McCravy)

given the rational function r(x)=(x^3-x^2)/x^3-3x-2) find the x and y intercepts find... (answered by lwsshak3)

Explain how the graph of R(x)= -3tan(1/2x) is related to the graph of the basic... (answered by lwsshak3)

Using the concepts of asymptotes analyze the graph of a rational function: 1) R(X)=x^2... (answered by Alan3354,greenestamps)