what is the end behavior of the graph of the polynomial function $f(x) = -x^{5} + 9x^{4} - 18x^{3}$?\nas $x…

what is the end behavior of the graph of the polynomial function $f(x) = -x^{5} + 9x^{4} - 18x^{3}$?\nas $x \\to -\\infty, y \\to -\\infty$ and as $x \\to \\infty, y \\to -\\infty$.\nas $x \\to -\\infty, y \\to -\\infty$ and as $x \\to \\infty, y \\to \\infty$.\nas $x \\to -\\infty, y \\to \\infty$ and as $x \\to \\infty, y \\to -\\infty$.\nas $x \\to -\\infty, y \\to \\infty$ and as $x \\to \\infty, y \\to \\infty$.

what is the end behavior of the graph of the polynomial function $f(x) = -x^{5} + 9x^{4} - 18x^{3}$?\nas $x \\to -\\infty, y \\to -\\infty$ and as $x \\to \\infty, y \\to -\\infty$.\nas $x \\to -\\infty, y \\to -\\infty$ and as $x \\to \\infty, y \\to \\infty$.\nas $x \\to -\\infty, y \\to \\infty$ and as $x \\to \\infty, y \\to -\\infty$.\nas $x \\to -\\infty, y \\to \\infty$ and as $x \\to \\infty, y \\to \\infty$.

Answer

Explanation:

Step1: Identify leading term

The leading term of $f(x)$ is $-x^5$.

Step2: Check degree & sign

Degree is 5 (odd), leading coefficient is $-1$ (negative).

Step3: Analyze $x\to\infty$

For odd degree, negative leading coefficient: as $x\to\infty$, $-x^5\to-\infty$, so $y\to-\infty$.

Step4: Analyze $x\to-\infty$

For odd degree, negative leading coefficient: as $x\to-\infty$, $-(-\infty)^5 = -(-\infty) = \infty$, so $y\to\infty$.

Answer:

As $x \to -\infty, y \to \infty$ and as $x \to \infty, y \to -\infty$.