$13 / 26$ 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 \[ \begin{array}{l} s(x) \rightarrow \square \text { as } x \rightarrow-\infty \\ s(x) \rightarrow \square \text { as } x \rightarrow \infty \end{array} \]
Solution
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: \[\boxed{\begin{array}{l} s(x) \rightarrow \infty \text { as } x \rightarrow-\infty \\ s(x) \rightarrow \infty \text { as } x \rightarrow \infty \end{array}}\]
