Question

For the following, Find the A) domain; B) the y-intercept; and C) all vertical and horizontal asymptotes.

y= (x^3+3x^2)/(x^4-4x^2)

Answer 1

A) domain is all reals except where the denominator is equal to zero.
B) plug in the values for A
C). Vertical asymptotes of a rational function (polynomial over another polynomial) can
potentially occur only if the denominator turns into 0
a horizontal asymptote defned by the ratio of the leading coecients

Answer 2

\[A)x^4-4x^2=x^2(x-2)(x+2)\] thus x can not equal 0,2,-2
B) to find the y intercept set x=0 which's not in the domain, hence we don't have one
C) the vertical asymptotes occur when the limit to some point is infinity, in this case the zeroes of the denominator, except x=0 cause the x's in the fraction cancel with each other when finding the limit to 0
and the HA asypmtote is the limit to infinity which is 0