Question

How do you find the asymptotes for `f(x)=x /( 4x^2+7x-2)`?

Answer 1

vertical asymptotes x = -2 , `x = 1/4`
horizontal asymptote y = 0

Explanation:

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

solve : `4x^2+7x-2=0 → (4x-1)(x+2)=0`

`rArr x = -2 , x=1/4 " are the asymptotes "`

Horizontal asymptotes occur as `lim_(x to +- oo) , f(x) to 0`

If the degree of the numerator < degree of the denominator then the equation is always y = 0
graph{x/(4x^2+7x-2) [-10, 10, -5, 5]}