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

1 Answer
Nov 12, 2016

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]}