Question

How do you find the Vertical, Horizontal, and Oblique Asymptote given `h(x)=(x^2-4 )/( x )`?

Answer 1

One vertical asymptote `x=0` and one oblique asymptote `y=x`

Explanation:

In `h(x)=(x^2-4)/x`,

vertical asymptotes are obtained by putting denominator equal to zero.

Hence `x=0` is the only vertical asymptote.

As the highest degree of numerator is `x^2` and of denominator `x` are not equal, there is no horizontal asymptote. But it is just one degree higher than that of denominator,

hence we have one oblique asymptote given by `y=x^2/x=x`

graph{(x^2-4)/x [-16, 16, -8, 8]}