Question

How do you find the asymptotes for `h(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 , set the denominator to zero.

hence : x = 0 is the asymptote

Horizontal asymptotes occur when the degree of the numerator is ≤ to the degree of the denominator. This is not so here , hence there are no horizontal asymptotes.

Oblique asymptotes occur when the degree of the numerator > than the degree of the denominator. This is the case here.

divide numerator by x

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

As`x tooo , 4/x to 0 " and " y to x`

`rArr y = x " is the asymptote "`

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