The given polynomial is:
[tex]f(x)=-5x^3+3x^2+x-9[/tex]
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:
[tex]-5x^3[/tex]
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:
[tex]\begin{gathered} x\to-\infty,f(x)\to+\infty\text{ and} \\ x\to+\infty,f(x)\to-\infty \end{gathered}[/tex]
The leading coefficient of this polynomial is -5, the sign is negative.
Thus, the answer is: option D.
