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.
\(\boxed{\text{As } x \rightarrow \infty, y \rightarrow -\infty}\)
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 :\(\boxed{\text{As } x \rightarrow \infty, y \rightarrow -\infty}\)