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

Nov 12, 2016

The vertical asymptote is $x = - \frac{1}{4}$
The horizontal asymptote is $y = - \frac{5}{4}$
There are no oblique asymptotes

#### Explanation:

As we cannot divide by $0$, the vertical asymptote is $x = - \frac{1}{4}$

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

${\lim}_{x \to - \infty} f \left(x\right) = {\lim}_{x \to - \infty} \frac{- 10 x}{8 x} = {\lim}_{x \to - \infty} - \frac{5}{4} = - \frac{5}{4}$

So, $y = - \frac{5}{4}$ is a horizontal asymptote

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