Explanation

• Horizontal asymptote: y = L, lim (x → ±∞) f(x) = L

Example:
f(x) = 3x/(x+1) → lim x→∞ = 3 → horizontal asymptote y = 3

Quiz

1. What is horizontal asymptote?

2. lim x→∞ 5x/(2x+1) = ?

3. Does function cross horizontal asymptote?

4. Can lim x→−∞ differ from +∞?

5. f(x) = 1/x → horizontal asymptote?

Answer Key

1. y = L as x → ±∞

2. 5/2

3. Yes, sometimes

4. Yes

5. y = 0