Step-by-step explanation:
f(x) = x (x – 4) (x + 2)⁴
The zeros are x = 0, 4, and -2.
When x = ∞, f(x) = ∞ (∞) (∞)⁴ = ∞.
When x = -∞, f(x) = -∞ (-∞) (-∞)⁴ = ∞.
Here's another way of looking at it:
f(x) has a leading coefficient of 1×1×1=1 and a power of 1+1+4=6. Since the leading coefficient is positive, and the power is even, f(x) approaches ∞ in both directions.
