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

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

anonymous · Answer

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

anonymous · Answer

to find the vertical asymptotes, set 
$$x^2-4=0$$ and solve for $x$

anonymous · Answer

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,
$$y=2$$