Question

the function f(x) is defined below. what is the end behavior of f(x)? f(x)= - 392 + 399x - 7x^3 answer attempt 1 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

The polynomial $f(x)=-7x^{3}+399x - 392$ is of degree $n = 3$ (the highest power of $x$), and the leading coefficient $a=-7$.

Step2: Determine end - behavior based on degree and leading coefficient

For a polynomial $y = a x^{n}$ with $n$ odd and $a<0$:
As $x\to-\infty$, $y\to\infty$ because $(-\infty)^{3}=-\infty$ and $a = - 7$ makes $y=-7\times(-\infty)=\infty$.
As $x\to\infty$, $y\to-\infty$ because $\infty^{3}=\infty$ and $y=-7\times\infty=-\infty$.
So, $\lim_{x\to-\infty}f(x)=\infty$ and $\lim_{x\to\infty}f(x)=-\infty$.

Answer:

The degree of the polynomial is $3$, and the leading coefficient is $-7$. The pair of limits representing the end - behavior is $\lim_{x\to-\infty}f(x)=\infty$, $\lim_{x\to\infty}f(x)=-\infty$