How to find the asymptotes of #f(x) =(-7x + 5) / (x^2 + 8x -20)# ?

1 Answer
Feb 4, 2016

Answer:

There are two kinds of asymptotes. The vertical ones are when the part under the fraction bar approaches zero.

Explanation:

You can factor #x^2+8x-20=(x+10)(x-2)#
Now you can expect asymptotes at #x=-10andx=2#

For the horizontal asymptote we make #x# as large as we want, both positive and negative. The function begins to look more and more like:
#(-7x)/(x^2+8x)# as the #+5and-20# don't matter anymore

If we cross out the #x#'s it's more like:
#-7/x# as the #+8# doesn't matter as compared to the size of #x#
As #x# gets larger, #f(x)# gets smaller, or, in 'the language':
#lim_(x->oo) f(x)=0 and lim_(x->-oo) f(x)=0#
graph{(-7x+5)/(x^2+8x-20) [-32.48, 32.47, -16.23, 16.26]}