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

1 Answer
Apr 12, 2016

vertical asymptotes x = - 4 , # x = 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

# 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 = 0

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