# How do you find the asymptotes for #(2x^2 - x - 38) / (x^2 - 4)#?

##### 1 Answer

vertical asymptotes at x = ± 2

horizontal asymptote at y = 2

#### Explanation:

As the denominator of a rational function tends to 0 there

will be a vertical asymptote.solve

#(x^2 - 4) =0 #

[horizontal asymptotes occur when

# lim_(x→±∞) f(x) → 0# ]when the degree of the numerator and denominator are equal

the equation can be found by taking the ratio of

leading coefficients.

In this question they are equal , both of degree 2

and so

# y = 2/1 rArr y = 2 # The graph shows the asymptotes.

graph{(2x^2-x-38)/(x^2-4) [-10, 10, -5, 5]}