How do you find vertical, horizontal and oblique asymptotes for # (x^4 - 8x^2 +16) / x^2#?

1 Answer
Jan 3, 2017

Answer:

The vertical asymptote is #x=0#
No horizontal asymptote
No slant asymptote

Explanation:

Let's rewrite the expression

#(x^4-8x^2+16)/x^2#

Let #f(x)=(x^4-8x^2+16)/x^2#

The domain of #f(x)# is #D_f(x)=RR-{0} #

As you canot divide by #0#, #x!=0#

#lim_(x->+-oo)f(x)=lim_(x->+-oo)x^4/x^2=lim_(x->+-oo)x^2=+oo#

graph{(y-(x^4-8x^2+16)/(x^2))(y-1000x)=0 [-10, 10, -5, 5]}