Problem 6. (1 point) Determine the end behavior for $y=-4 x^{9}+2 x^{4}+4 x$. - As $x \rightarrow-\infty, y \rightarrow \square$ help (numbers) - As $x \rightarrow \infty, y \rightarrow \square$ help (numbers) Note: You can earn partial credit on this problem.
Solution
Step 1 ：The given function is \(y=-4 x^{9}+2 x^{4}+4 x\).
Step 2 ：The degree of the polynomial is 9, which is odd, and the leading coefficient is -4, which is negative.
Step 3 ：For polynomials with odd degree, the end behavior is determined by the sign of the leading coefficient.
Step 4 ：Since the leading coefficient is negative, as \(x \rightarrow \infty\), \(y \rightarrow -\infty\).
Step 5 ：Since the degree is odd, as \(x \rightarrow -\infty\), \(y \rightarrow \infty\).
Step 6 ：So, the end behavior of the function is: as \(x \rightarrow-\infty, y \rightarrow \infty\) and as \(x \rightarrow \infty, y \rightarrow -\infty\).
Step 7 ：\(\boxed{\text{As } x \rightarrow-\infty, y \rightarrow \infty}\)
Step 8 ：\(\boxed{\text{As } x \rightarrow \infty, y \rightarrow -\infty}\)
