# What are the asymptotes of f(x)=-x/((2x-3)(x+4)) ?

Apr 12, 2016

vertical asymptotes x = - 4 , $x = \frac{3}{2}$
horizontal asymptote y = 0

#### Explanation:

Vertical asymptotes occur as the denominator of a rational function tends to zero. To find the equation/s let the denominator equal zero.

solve : (2x - 3 )(x +4) = 0

$\Rightarrow x = - 4 , x = \frac{3}{2} \text{ are the asymptotes }$

Horizontal asymptotes occur as ${\lim}_{x \to \pm \infty} f \left(x\right) \to 0$

When the degree of the numerator < degree of the denominator , as is the case here the the equation is always
y = 0

Here is the graph of f(x).
graph{-(x)/((2x-3)(x+4)) [-10, 10, -5, 5]}