Question

I NEED HELP PLEASE, THANKS! :) Determine the zeros for and the end behavior of f(x) = x(x – 4)(x + 2)^4.

Answer 1

Answer: a) zeros: x = {0, 4, -2}

b) as x → ∞, y → ∞

as x → -∞, y → ∞

Explanation:

I think you mean (a) find the zeros and (b) describe the end behavior

(a) Find the zeros by setting each factor equal to zero and solving for x:

x (x - 4) (x + 2)⁴ = 0

• x = 0 Multiplicity of 1 --> odd multiplicity so it crosses the x-axis

• x = 4 Multiplicity of 1 --> odd multiplicity so it crosses the x-axis

• x = -2 Multiplicity of 4 --> even multiplicity so it touches the x-axis

Degree = 6

(b) End behavior is determined by the following two criteria:

1. Sign of Leading Coefficient (Right side): Positive is ↑, Negative is ↓
2. Degree (Left side): Even is same direction as right side, Odd is opposite direction of right side

Sign of the leading coefficient is Positive so right side goes UP

as x → ∞, y → ∞

Degree of 6 is Even so Left side is the same direction as right (UP)

as x → -∞, y → ∞