Question

The graph of has a horizontal asymptote at y =

Answer 1

It looks like the function is missing from your question — could you paste the function whose graph you mean?

Meanwhile, here are quick rules you can use to find horizontal asymptotes:

- More generally: compute the limits L+ = lim_{x→∞} f(x) and L− = lim_{x→−∞} f(x). If L+ (or L−) exists and is finite, then y = L+ (or y = L−) is a horizontal asymptote on the right (or left).
- For rational functions f(x) = p(x)/q(x) with deg p = n and deg q = m:
- If n < m → y = 0.
- If n = m → y = (leading coefficient of p)/(leading coefficient of q).
- If n > m → no horizontal asymptote (there may be an oblique or higher-degree polynomial asymptote).
- For other types: use limits. Example: y = a + b e^{cx} → tends to a as x→∞ if c < 0.

Examples:
- f(x) = (3x^2 + 1)/(2x^2 − 5) → degs equal, horizontal asymptote y = 3/2.
- f(x) = (x+1)/(x^2+1) → deg numerator < denominator → y = 0.

If you paste the specific function, I’ll compute the horizontal asymptote(s).