Question

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

Answer 1

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]}