Question

For the given function, find the vertical and horizontal asymptote(s) (if there are any).

f(x) = the quantity two x squared plus one divided by the quantity x squared minus four

Answer 1

\[f(x)=\frac{2x^2+1}{x^2-4}\]?

Answer 2

to find the vertical asymptotes, set
\[x^2-4=0\] and solve for \(x\)

Answer 3

horizontal:
since the degree of the top and bottom are the same (they are both degree 2) the horizontal asymptote is the ratio of the leading coefficients,
\[y=2\]