Question

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

Answer 1

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]}