Question

the function f(x) is defined below. what is the end behavior of f(x)? f(x)=-624x + 108x^{2}+1152 - 6x^{3} answer attempt 2 out of 2 the degree of the polynomial is , and the leading coefficient is 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 degree and leading - coefficient

For the polynomial $f(x)=-6x^{3}+108x^{2}-624x + 1152$, the degree $n = 3$ (the highest power of $x$) and the leading - coefficient $a=-6$.

Step2: Determine end - behavior using degree and leading - coefficient

When the degree $n$ of a polynomial is odd and the leading coefficient $a<0$, as $x\to-\infty$, $y = f(x)\to\infty$ and as $x\to\infty$, $y = f(x)\to-\infty$. Mathematically, $\lim_{x\to-\infty}f(x)=\infty$ and $\lim_{x\to\infty}f(x)=-\infty$.

Answer:

The degree of the polynomial is $3$, and the leading coefficient is $-6$. The pair of limits representing the end - behavior is $\lim_{x\to-\infty}f(x)=\infty$, $\lim_{x\to\infty}f(x)=-\infty$