Question

How do you find the asymptotes for `f(x)=( -10x+3)/(8x+2)`?

Answer 1

vertical asymptote `x= -1/4`

horizontal asymptote `y = -5/4`

Explanation:

vertical asymptotes occur as the denominator of a rational

function tends to zero.

solving 8x + 2 = 0 will give the asymptote

hence `8x = -2 → x = - 2/8 rArr x = -1/4`

horizontal asymptotes occur as `lim_(x→±∞)f(x) → 0`

If the degree of numerator and denominator are equal

Which they are in this case , both of degree 1. then the

equation can be found by taking the ratio of leading

coefficients.

`y = -10/8 = -5/4 rArr y = -5/4`

Here is the graph 0f f(x)
graph{(-10x+3)/(8x+2) [-20, 20, -10, 10]}