How do you find any asymptotes of #f(x)=(x+3)/(x^2-4)#?
1 Answer
There are two vertical asymptotes at
There is a horizontal asymptote at 0 as
There is a horizontal asymptote at 0 as
Explanation:
Vertical Asymptotes
These occur when the denominator is zero
Horizontal Asymptotes
We also need to examine the behaviour as
Now for large
We have,
and so, for large
so, as
and, as
Summary
There are two vertical asymptotes at
There is a horizontal asymptote at 0 as
There is a horizontal asymptote at 0 as
The graph validates this;
graph{(x+3)/((x+2)(x-2)) [-10, 10, -5, 5]}
