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

##### 1 Answer

Apr 12, 2016

vertical asymptotes x = - 4 ,

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

# rArr x = -4 , x = 3/2" are the asymptotes "# Horizontal asymptotes occur as

#lim_(xto+-oo) f(x) to 0 # When the degree of the numerator < degree of the denominator , as is the case here the the equation is always

y = 0Here is the graph of f(x).

graph{-(x)/((2x-3)(x+4)) [-10, 10, -5, 5]}