How to find the asymptotes of R(x)=(3x+5) / (x-6)?

Jun 21, 2018

Vertical: $x = 6$
Horizontal: $y = 3$

Explanation:

Vertical asymptotes are values for which the function is undefined. Our function is undefined when the denominator is equal to zero.

Setting it equal to zero, we get

$x = 6$. This is our vertical asymptote.

To find our horizontal asymptote, we need to analyze the degrees of the function.

We have the same degree on the top and bottom, so the variables cancel. As a horizontal asymptote, we're left with

$y = 3$

Hope this helps!