Question

f(x)=81x - 162 - 9x^{2}
answer
attempt 2 out of 2
the degree of the polynomial is odd, and the leading coefficient is positive.
choose which pair of limits below represents the end - behavior:
lim_{x→ - ∞}f(x)=∞, lim_{x→∞}f(x)=∞
lim_{x→ - ∞}f(x)= - ∞, lim_{x→∞}f(x)=∞
lim_{x→ - ∞}f(x)=∞, lim_{x→∞}f(x)= - ∞
lim_{x→ - ∞}f(x)= - ∞,
lim_{x→∞}f(x)= - ∞

Explanation:

Step1: Identify polynomial form

Rewrite $f(x)= - 9x^{2}+81x - 162$.

Step2: Determine degree and leading - coefficient

The degree of the polynomial $f(x)$ is 2 (even) and the leading coefficient is - 9 (negative).
For a polynomial $y = a_nx^n+\cdots+a_0$ with $n$ even and $a_n<0$, as $x\to\pm\infty$, $y\to-\infty$.
The correct limits for the end - behavior are $\lim_{x\to-\infty}f(x)=-\infty$ and $\lim_{x\to\infty}f(x)=-\infty$.

Answer:

$\lim_{x\to-\infty}f(x)=-\infty,\lim_{x\to\infty}f(x)=-\infty$