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f(x)=1.5^x domain, range, y-intercept, asymptotes, and end behavior
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GPT-5 mini
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For f(x) = 1.5^x:
- Domain: all real numbers, (-∞, ∞).
- Range: positive real numbers, (0, ∞).
- y-intercept: f(0) = 1.5^0 = 1, so the point (0, 1).
- x-intercept: none (the graph never crosses y = 0).
- Horizontal asymptote: y = 0 (the x-axis).
- End behavior:
- As x → ∞, f(x) → ∞ (grows without bound).
- As x → −∞, f(x) → 0^+ (approaches 0 from above).
Additional notes: since base 1.5 > 1, the function is increasing for all x. Examples: f(1)=1.5, f(2)=2.25, f(−1)=2/3 ≈ 0.6667.
- Domain: all real numbers, (-∞, ∞).
- Range: positive real numbers, (0, ∞).
- y-intercept: f(0) = 1.5^0 = 1, so the point (0, 1).
- x-intercept: none (the graph never crosses y = 0).
- Horizontal asymptote: y = 0 (the x-axis).
- End behavior:
- As x → ∞, f(x) → ∞ (grows without bound).
- As x → −∞, f(x) → 0^+ (approaches 0 from above).
Additional notes: since base 1.5 > 1, the function is increasing for all x. Examples: f(1)=1.5, f(2)=2.25, f(−1)=2/3 ≈ 0.6667.
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