Question

end behavior of 𝑓⁡(𝑥)=3^x

Answer 1

For f(x) = 3^x:

- As x → ∞: f(x) → ∞ (grows without bound).
lim_{x→∞} 3^x = ∞.

- As x → −∞: f(x) → 0 from above (approaches 0 but never reaches it).
lim_{x→−∞} 3^x = 0^+.

Consequences: horizontal asymptote y = 0, domain (−∞, ∞), range (0, ∞). The function is always positive and strictly increasing (f'(x) = ln(3)·3^x > 0).