Question

How do you find vertical, horizontal and oblique asymptotes for `f(x) = (x-4)/ (x^2-1)`?

Answer 1

vertical asymptotes x = ± 1
horizontal asymptote y = 0

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 - 1 = 0 → (x - 1 )(x + 1 ) = 0`

`rArr x = ± 1 " 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 case, degree of numerator 1 and degree of denominator 2 . Then the equation is always y = 0.

Here is the graph of the function.
graph{(x-4)/(x^2-1) [-10, 10, -5, 5]}