Question

How do you find the slant asymptote of `y=(x^2)/(2x^2-8)`?

Answer 1

No slant asymptote exists, but there is the horizontal asymptote `y=1/2.`

Explanation:

The numerator and denominator are of the same degree (degree `2`) -- no slant asymptote exists in such cases.

Rather, there is a horizontal asymptote given by dividing the coefficients of the leading terms (terms of highest degree), in this case, `y=1/2.`