15. Determine the zeros for and the end behavior of f(x) = x(x – 4)(x + 2)^4.

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.