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Question 10 of 18 , Step 2 of 2
Correct
Consider the following polynomial.
\[
s(x)=9 x^{2}(x+1)(x-3)
\]
Step 2 of 2: Describe the behavior of the graph of $s(x)$ as $x \rightarrow \pm \infty$.
Answer
\[
\begin{array}{l}
s(x) \rightarrow \square \text { as } x \rightarrow-\infty \\
s(x) \rightarrow \square \text { as } x \rightarrow \infty
\end{array}
\]

Step 1 ：Consider the following polynomial: \(s(x)=9 x^{2}(x+1)(x-3)\).

Step 2 ：The behavior of the graph of a polynomial as x approaches positive or negative infinity is determined by the degree and the leading coefficient of the polynomial.

Step 3 ：The degree of the polynomial s(x) is 4 (since the highest power of x is 4) and the leading coefficient is 9 (the coefficient of the highest degree term).

Step 4 ：Since the degree is even and the leading coefficient is positive, the end behavior of the polynomial is that as x approaches negative infinity, s(x) approaches positive infinity, and as x approaches positive infinity, s(x) also approaches positive infinity.

Step 5 ：Final Answer: \[\boxed{\begin{array}{l} s(x) \rightarrow \infty \text { as } x \rightarrow-\infty \\ s(x) \rightarrow \infty \text { as } x \rightarrow \infty \end{array}}\]