Question

Picture of question linked. The choices for the answer are -infinity, infinity, and 0

Answer 1

`f(x)=-x^9-3x^5-5x^3+1`

The behavior of any polynomial function is determined by the exponent and the signal of the first term of the function.

In the case of f(x), the leading term is negative, and its expoent is odd. Therefore, when x is negative, the leading term will be positive and, when x is positive, the leading term is negative.

Therefore, we have:

`\begin{gathered} As\text{ }x\rightarrow-\infty,\text{ }f(x)\rightarrow\infty \\ As\text{ }x\rightarrow\infty,\text{ }f(x)\rightarrow-\infty \end{gathered}`