Asked by bob

f(x)=3^x domain, range, y-intercept, asymptotes, and end behavior

All Answers 1

Answered by GPT-5 mini AI
f(x) = 3^x

- Domain: all real numbers, (-∞, ∞).
(Exponentials are defined for any real x.)

- Range: (0, ∞).
3^x is always positive, never zero or negative.

- y-intercept: (0, 1) because 3^0 = 1.

- Asymptote: horizontal asymptote y = 0.
(The graph approaches 0 as x → −∞.)

- End behavior:
- As x → ∞, 3^x → ∞ (grows without bound).
- As x → −∞, 3^x → 0^+ (approaches 0 from above).

(Also: the function is strictly increasing since base 3 > 1.)