Question

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)

Answer 1

I assume f(x) = 4(1.5)^x.

Key facts
- Domain: (-∞, ∞)
- Range: (0, ∞)
- y-intercept: f(0) = 4, so (0, 4)
- Horizontal asymptote: y = 0
- Constant percent rate of change: growth factor 1.5 → 50% increase per 1 unit increase in x
- Interval behavior: increasing for all x (increasing on (-∞, ∞)); as x → ∞, f(x) → ∞; as x → -∞, f(x) → 0+

Sample points (for sketching)
- x = -2: f = 4(1.5)^(-2) = 4(0.4444) ≈ 1.7778
- x = -1: f ≈ 2.6667
- x = 0: f = 4
- x = 1: f = 6
- x = 2: f = 9

Graph description: passes through (0,4), (1,6), (2,9), approaches the x-axis on the left (never touches), and rises without bound on the right.