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.

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.