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

1 Answer
May 1, 2016

Answer:

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]}