# How do you find the Vertical, Horizontal, and Oblique Asymptote given #g(t) = (t − 6) / (t^(2) + 36)#?

##### 1 Answer

Aug 7, 2018

This function only has a horizontal asymptote

#### Explanation:

Given:

#g(t) = (t-6)/(t^2+36)#

Note that the denominator is positive for any real value of

Hence this rational function has no vertical asymptotes and no holes.

The degree of the denominator is also greater than the numerator. So it has no blique asymptotes - only the horizontal asymptote

#lim_(t->+-oo) (t-6)/(t^2+36) = lim_(t->+-oo) (1/t-6/t^2)/(1+36/t^2) = (0-0)/(1+0) = 0#

graph{(x-6)/(x^2+36) [-20, 30, -0.3, 0.3]}