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

f(x) = 4(1.5)^x

Key features
- Domain: (-∞, ∞)
- Range: (0, ∞)
- y-intercept: f(0) = 4 → point (0, 4)
- Horizontal asymptote: y = 0
- Constant percent rate of change: factor 1.5 per 1 unit of x → 50% growth per unit (exponential growth)
- Monotonic behavior: increasing on (-∞, ∞); as x → ∞, f(x) → ∞; as x → -∞, f(x) → 0^+

A few plot points
- f(-2) = 4(1.5)^(-2) ≈ 1.78
- f(-1) ≈ 2.67
- f(0) = 4
- f(1) = 6
- f(2) = 9

Graph description: an exponential growth curve crossing (0,4), rising to the right, approaching the x-axis on the left (but never touching it).