SOLUTION: What is the equation of the slant asymptote for R(x) = x^2-6x+8/x-4? a. R(x) = x – 2 b. R(x) = 1 c. R(x) = -5x + 2 d. There is no slant asymptote

Algebra ->  Equations -> SOLUTION: What is the equation of the slant asymptote for R(x) = x^2-6x+8/x-4? a. R(x) = x – 2 b. R(x) = 1 c. R(x) = -5x + 2 d. There is no slant asymptote      Log On


   

Question 152873: What is the equation of the slant asymptote for R(x) = x^2-6x+8/x-4?
a. R(x) = x – 2
b. R(x) = 1
c. R(x) = -5x + 2
d. There is no slant asymptote
Answer by Edwin McCravy(20055) About Me  (Show Source):
You can put this solution on YOUR website!
What is the equation of the slant asymptote for R%28x%29+=+%28x%5E2-6x%2B8%29%2F%28x-4%29?
a. R%28x%29+=+x+%96+2
b. R%28x%29+=+1
c. R%28x%29+=+-5x+%2B+2
d. There is no slant asymptote

A rational function has a slant asymptote if and only if it meets
both these conditions:

1. The degree of the the numerator is 1 more than the degree of
the denominator.

2. When the denominator is divided into the numerator, a non-zero
remainder is obtained.  

3. If so then y+=+quotient is the equation of
the slant asymptote.

--------------------------------------

R%28x%29+=+%28x%5E2-6x%2B8%29%2F%28x-4%29?

The degree of the numerator is 2 (largest power of x is 2)
The degree of the denominator is 1 (largest power of x is 1)

Therefore it meets the first condition. Let's see if it meets
the second condition:

            x - 2
x - 4)x² - 6x + 8
      x² - 4x
          -2x + 8
          -2x + 8
                0

No, it leaves a zero remainder.  So R(x) does not have a
slant asymptote.

The correct choice is d
Edwin