Question 1084114: Function: (x^2+x-12)/(x^2-4)
Identify horizontal asymptote, vertical asymptote, x-intercepts, and holes. If possible, graph.
Thanks! Answer by KMST(5328) (Show Source):
You can put this solution on YOUR website!
It is clear that the function is not defined for x=2 and for x=-2.
As x approaches those values the denominator approaches zero,
while the numerator approaches some non-zero value.
That means that as x approaches 2 or -2,
the absolute value of the function increases without bounds.
So, x=2, and x=z2 are vertical asymptotes.
Looking at the function a different way we see that ,
we see that as the absolute value of x increases,
the term approaches zero,
meaning that the function's value approaches 1.
So, y=1 is the horizontal asymptote.
