Determine the equations of any horizontal and vertical asymptotes of .
A) horizontal: ; vertical:
B) horizontal: ; vertical:
C) horizontal: ; vertical: none
D) horizontal: ; vertical:
E) horizontal: ; vertical:

Question

Determine the equations of any horizontal and vertical asymptotes of  .
A) horizontal: ; vertical: 
B) horizontal: ; vertical: 
C) horizontal: ; vertical: none 
D) horizontal: ; vertical: 
E) horizontal: ; vertical:

Quizplus · Accepted Answer

There is a horizontal asymptote when the degree of the numerator and denominator are the same. In this case, both the numerator and denominator have a degree of 2. Therefore, there is a horizontal asymptote at y = (leading coefficient of numerator) / (leading coefficient of denominator) = 11/(-6) = -11/6 = -1.833...

There is a vertical asymptote when the denominator equals zero. In this case, the denominator is (x-3)(x+2). Therefore, there are vertical asymptotes at x = 3 and x = -2. None of the other answer choices have the correct horizontal and vertical asymptotes.

Determine the Equations of Any Horizontal and Vertical Asymptotes of