Find vertical and horizontal asymptotes.
$f ( x ) = \frac { 9 + 6 x } { 6 + x }$
A)Vertical asymptote: x = -6Horizontal asymptote: y = 6
B)Vertical asymptote: x = 0Horizontal asymptote: y = -6
C)Vertical asymptote: x = 6Horizontal asymptote: y = -6
D)Vertical asymptote: x = 0Horizontal asymptote: y = 6
E)Vertical asymptote: x = -6Horizontal asymptote: y = 0

Question

Find vertical and horizontal asymptotes. 
 $f ( x ) = \frac { 9 + 6 x } { 6 + x }$  
A)Vertical asymptote: x = -6Horizontal asymptote: y = 6
B)Vertical asymptote: x = 0Horizontal asymptote: y = -6
C)Vertical asymptote: x = 6Horizontal asymptote: y = -6
D)Vertical asymptote: x = 0Horizontal asymptote: y = 6
E)Vertical asymptote: x = -6Horizontal asymptote: y = 0

Quizplus · Accepted Answer

Vertical asymptotes occur where the denominator of a rational function is zero (as long as the numerator is not zero at the same point, which would indicate a hole). For $f(x) = \frac{9 + 6x}{6 + x}$, setting the denominator equal to zero gives $6 + x = 0$, or $x = -6$. Horizontal asymptotes for rational functions where the degree of the numerator and denominator are the same are found by dividing the leading coefficients. Here, both the numerator and denominator are first degree, and the leading coefficients are 6 (numerator) and 1 (denominator), so the horizontal asymptote is $y = \frac{6}{1} = 6$.

Find Vertical and Horizontal Asymptotes f(x)=9+6x6+xf ( x ) = \frac { 9 + 6 x } { 6 + x }f(x)=6+x9+6x​

Find Vertical and Horizontal Asymptotes $f ( x ) = \frac { 9 + 6 x } { 6 + x }$