Question

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

Answer 1

vertical asymptote x = 0
oblique asymptote y = x

Explanation:

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

`rArr x = 0 " is the asymptote "`

There are no horizontal asymptotes , since degree of numerator is greater than degree of numerator. However , this does mean that there is an oblique asymptote.

divide all terms on numerator by x

hence `y = x^2/x - 4/x = x - 4/x`

As x → ±∞ , `4/x → 0 and y → x`

`rArr y = x " is the asymptote "`

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