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

Feb 2, 2016

vertical asymptote $x = - \frac{1}{4}$

horizontal asymptote $y = - \frac{5}{4}$

#### 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.

$y = - \frac{10}{8} = - \frac{5}{4} \Rightarrow y = - \frac{5}{4}$

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