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 when the denominator of a rational function tends to zero. To find the equation/s let the denominator equal 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→±∞) f(x) → 0`

If the degree of the numerator is less than the degree of the denominator, as in this question, then the equation of the asymptote is always y = 0.

Here is the graph of f(x)
graph{x/(4x^2+7x-2) [-10, 10, -5, 5]}