Find all horizontal and vertical asymptotes of the function $y ( x ) = \frac { 6 } { x - 6 }$ .
A) HA: $x - a x i s$
$\mathrm { VA } : x = 6$
B) $\mathrm { HA: } : y = 0$
$\mathrm { VA}$ : $x = - 6$
C) $\mathrm { HA }$ : none
$\mathrm { VA } : x = 6$
D) $\mathrm { HA }$ : none
$\mathrm { VA } : x = 1$
E) $\mathrm { HA } : y = 6$
$\mathrm { VA } : x = 6$

Question

Find all horizontal and vertical asymptotes of the function $y ( x ) = \frac { 6 } { x - 6 }$ .
A) HA: $x - a x i s$
$\mathrm { VA } : x = 6$ 
B) $\mathrm { HA: } : y = 0$
$\mathrm { VA}$ : $x = - 6$ 
C) $\mathrm { HA }$ : none
$\mathrm { VA } : x = 6$ 
D) $\mathrm { HA }$ : none
$\mathrm { VA } : x = 1$ 
E) $\mathrm { HA } : y = 6$
$\mathrm { VA } : x = 6$

Quizplus · Accepted Answer

To find the horizontal asymptote, we look at what happens to the function as $x$ gets very large or very small. As $x$ gets very large or very small, $\frac{6}{x-6}$ approaches 0, so the horizontal asymptote is $y=0$. 
To find the vertical asymptote, we look at what happens as $x$ approaches the value that makes the denominator equal to 0. In this case, the denominator is equal to 0 when $x=6$, so the vertical asymptote is the line $x=6$. The correct choice is A, which says that the horizontal asymptote is $x$-axis and the vertical asymptote is $x=6$.

Find All Horizontal and Vertical Asymptotes of the Function y(x)=6x−6y ( x ) = \frac { 6 } { x - 6 }y(x)=x−66​

Find All Horizontal and Vertical Asymptotes of the Function $y ( x ) = \frac { 6 } { x - 6 }$