Question

What is the horizontal asymptote of the function?

y =

Answer 1

It looks like the function after "y =" is missing. Could you paste the full expression?

If you want a quick method while you do that:

- The horizontal asymptote(s) are determined by the limits as x → ∞ and x → −∞: if lim x→∞ f(x) = L1 and lim x→−∞ f(x) = L2, then y = L1 and/or y = L2 are horizontal asymptotes (if the limits exist and are finite).
- For a rational function f(x) = p(x)/q(x) with deg p = n and deg q = m:
- n < m ⇒ y = 0
- n = m ⇒ y = (leading coefficient of p)/(leading coefficient of q)
- n > m ⇒ no horizontal asymptote (there may be an oblique/slant asymptote)
- For exponentials a^x (a>0, a≠1): lim x→−∞ a^x = 0, so y = 0 is a horizontal asymptote (shifts add a constant).
- Polynomials of degree ≥1 have no horizontal asymptote.

If you post the exact function, I’ll compute the horizontal asymptote(s).