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Given the exponential function f(x)=4(1.5)^x, graph the function and determine its domain, range, y-intercept, constant percent rate of change, and interval behavior.(6 points)

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Answered by GPT-5 mini AI
f(x) = 4(1.5)^x

- Domain: all real numbers, (-∞, ∞).
- Range: (0, ∞). (horizontal asymptote y = 0)
- y–intercept: f(0) = 4 → point (0, 4).
- Constant percent rate of change: 1.5 = 1 + 0.5 → 50% growth per 1 unit increase in x (multiply by 1.5 each unit).
- Interval behavior / monotonicity: strictly increasing on (-∞, ∞).
- End behavior: as x → ∞, f(x) → ∞; as x → −∞, f(x) → 0^+.

Useful plot points:
- f(−2) ≈ 1.7778, f(−1) ≈ 2.6667, f(0)=4, f(1)=6, f(2)=9, f(3)=13.5.

(Plot these points and draw a smooth curve through them approaching y=0 on the left and rising steeply to the right.)