Question

How do you find vertical, horizontal and oblique asymptotes for `(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.

hence : x = 0 is the asymptote

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

When the degree of the numerator is greater than the degree of the denominator, there will be no horizontal asymptotes , but there will be an oblique asymptote.

now `(x^2-4)/x = x^2/x - 4/x = x - 4/x`

As x→±∞ , `4/x → 0 " and " y → x`

`rArr y = x " is an oblique asymptote "`
graph{(x^2-4)/x [-10, 10, -5, 5]}