Question

the function f(x) is defined below. what is the end behavior of f(x)? f(x)=-63 + 54x+9x^{2} 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 of polynomial

The highest - power of $x$ in $f(x)=-63 + 54x+9x^{2}$ is 2, so the degree $n = 2$.

Step2: Identify leading coefficient

The coefficient of the term with the highest - power of $x$ is 9, so the leading coefficient $a = 9>0$.

Step3: Determine end - behavior

For a polynomial $y = a x^{n}$ with $n$ even and $a>0$, as $x\to-\infty$, $y\to\infty$ and as $x\to\infty$, $y\to\infty$. That is $\lim_{x\to-\infty}f(x)=\infty$ and $\lim_{x\to\infty}f(x)=\infty$.

Answer:

The degree of the polynomial is 2, and the leading coefficient is 9.
$\lim_{x\to-\infty}f(x)=\infty,\lim_{x\to\infty}f(x)=\infty$