Problem

Given a polynomial function \(f(x) = -3x^5 + 2x^3 - 9x + 4\), what is the end behavior of the function?

Answer

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Answer

According to the Leading Coefficient Test, if the degree of the polynomial is odd and the leading coefficient is negative, the function rises to the left and falls to the right.

Steps

Step 1 ：First, we need to identify the leading term of the polynomial function. In this case, the leading term is \(-3x^5\).

Step 2 ：The degree of the polynomial function is 5, which is odd, and the leading coefficient is -3, which is negative.

Step 3 ：According to the Leading Coefficient Test, if the degree of the polynomial is odd and the leading coefficient is negative, the function rises to the left and falls to the right.

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