Invent a rational function so that y=2 is a horizontal asymptote and there are no vertical asymptotes.?

Question

I just found this question I never got on my test last year... could anyone help explain it to me? I was thinking it had to be 2x/? but what I've tried doesn't work. Thanks in advance.

Answer 1

MANY exist...[2 x^2-9] / [ x^2 + 17] is one .

Answer 2

A good template to try is y = 2 + 1/f(x), where f(x) goes to infinity as x goes to infinity, but doesn't have any zeros.

OK. Try f(x) = 1+ x^2. I think that will do the job for you. ;)