Question

What describes the end behavior of the polynomial function?

Answer 1

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

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`.