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