Question

Which of the following describes the end behavior of the function

Answer 1

The given polynomial is:

`f(x)=-5x^3+3x^2+x-9`

The end behavior of a polynomial is given by its leading term (the term with the largest exponent).

The leading term of this polynomial is:

`-5x^3`

The rules for end behavior state:

- When the degree of the leading term is odd, the behavior of the function at both ends is opposite. (This polynomial has degree 3.)

- When the sign of the leading coefficient is negative, then:

`\begin{gathered} x\to-\infty,f(x)\to+\infty\text{ and} \\ x\to+\infty,f(x)\to-\infty \end{gathered}`

The leading coefficient of this polynomial is -5, the sign is negative.

Thus, the answer is: option D.