How do you find the Vertical, Horizontal, and Oblique Asymptote given #f(x)= (-10x+3)/(8x+2)#?

1 Answer
Nov 12, 2016

Answer:

The vertical asymptote is #x=-1/4#
The horizontal asymptote is #y=-5/4#
There are no oblique asymptotes

Explanation:

As we cannot divide by #0#, the vertical asymptote is #x=-1/4#

There are no oblique asymptote as the degree of the numeratoris #=# the degree of the denominator.

#lim_(x->-oo)f(x)=lim_(x->-oo)(-10x)/(8x)=lim_(x->-oo)-5/4=-5/4#

So, #y=-5/4# is a horizontal asymptote

graph{(-10x+3)/(8x+2) [-5.03, 4.83, -2.66, 2.272]}