Question

What describes the end behavior of the polynomial function?

Answer 1

Answer:

$x \to +\infty$, $f(x) \to +\infty$ and $x \to -\infty$, $f(x) \to -\infty$.

Step-by-step explanation:

A polynomial is an algebraic function of the form:

$y = \Sigma_{i=0}^{n}c_{i}\cdot x^{i}$ (1)

Where:

$c_{i}$ - i-th Coefficient.

$x^{i}$ - i-th Power.

$n$ - Grade of the polynomial.

$y$ - Dependent variable.

Mathematically speaking, polynomials are unbounded functions, and from graphic we notice that polynomial is of order 3 due to the fact that function pass through the x axis three times, where each point is a root of the polynomial.

Then, we may conclude that:  

(i) $\lim_{n \to +\infty} f(x) = N.E.$

(ii) $\lim_{n \to - \infty} f(x) = N.E.$

Then, the right answer is: $x \to +\infty$, $f(x) \to +\infty$ and $x \to -\infty$, $f(x) \to -\infty$.