Question

How do you find the asymptotes for `F(x)=(x^2+x-12) /(x^2-4)`?

Answer 1

vertical asymptotes at x = ± 2
horizontal asymptote at y = 1

Explanation:

Vertical asymptotes occur as the denominator of a rational function tends to zero. To find the equation equate the denominator to zero.

solve `x^2 - 4 = 0 → (x-2)(x+2) = 0 → x = ± 2`

Horizontal asymptotes occur as`lim_(x→±∞) f(x) → 0`

If the degree of the numerator and denominator are equal ,as they are in this case, both of degree 2 then the equation can be found by taking the ratio of leading coefficients.

equation is `y = 1/1 = 1`

Here is the graph of the function to illustrate asymptotes.
graph{(x^2+x-12)/(x^2-4) [-10, 10, -5, 5]}