Question

HELP.

Answer 1

The degree and number of unique zeros of f(x) = (x – 5)(x + 3)(x – 1)² is:

Degree: 4; number of unique zeros: 3.

The end behavior of the polynomial is:

As x → –∞, f(x) → ∞ and as x → ∞, f(x) → ∞.

How to obtain the degree of the function?

The degree of the polynomial function is given by the sum of the multiplicities of the roots.

These roots are given as follows:

• x = 5 with a multiplicity of 1.

• x = -3 with a multiplicity of 1.

• x = 1 with a multiplicity of 2.

Hence the degree is:

1 + 1 + 2 = 4.

The unique zeros are the roots, hence there are three unique zeros, which is the same number of linear factors of the function.

What is the end behavior of the function?

The end behavior is the limit of the function as x goes to negative infinity and to positive infinite, hence:

• lim x -> -∞ f(x) = lim x -> -∞ x^4 = (-∞)^4 = ∞.

• lim x -> ∞ f(x) = lim x -> ∞ x^4 = (∞)^4 = ∞.

Learn more about the end behavior of a function at brainly.com/question/1365136

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