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

Mar 21, 2016

#### Answer:

vertical asymptotes , x = -2 , $x = \frac{1}{4}$
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

$\Rightarrow x = - 2 , x = \frac{1}{4} \text{ are the asymptotes }$

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]}