How do you find the asymptotes for #y = (8 x^2 + x - 2)/(x^2 + x - 72)#?

1 Answer
Mar 11, 2016

Answer:

Vertical asymptotes: #x=-8,x=9#
Horizontal asymptote: #y=8#

Explanation:

To find the vertical asymptotes of a rational equation, find when the equation's denominator equals #0#:

#x^2-x-72=0#

#(x-9)(x+8)=0#

#x=9,x=-8#

These are where vertical asymptotes will occur.

As for horizontal asymptotes, examine the degree of the numerator and denominator. They are both #2#. When the numerator and denominator of a rational function have the same degree, the horizontal asymptote can be found by dividing the two terms with the largest degree:

#(8x^2)/x^2=8#

Thus there is a horizontal asymptote at #y=8#.

We can check a graph:

graph{(8 x^2 + x - 2)/(x^2 + x - 72) [-13, 12, -50, 50]}