Question

the function f(x) is defined below. what is the end - behavior of f(x)?

f(x)=-120 + 50x-5x^{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\to -\infty}f(x)=\infty, lim_{x\to\infty}f(x)=\infty

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

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

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

Explanation:

Step1: Identify degree of polynomial

The highest - power of \(x\) in \(f(x)=- 120 + 50x-5x^{2}\) is \(2\), so the degree is even.

Step2: Identify leading coefficient

The coefficient of \(x^{2}\) is \(-5\), so the leading coefficient is negative.

Step3: Determine end - behavior

For a polynomial \(y = ax^{n}\) 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 even, and the leading coefficient is negative. The pair of limits is \(\lim_{x\to-\infty}f(x)=-\infty,\lim_{x\to\infty}f(x)=-\infty\)