Question

Determine the end behavior for function ƒ(x) = (x2 + 1)2 (2x – 3)

Answer 1

It's an odd-degree polynomial with a positive x^5 coefficient. The general shape is "/".

It goes to -∞ for large negative x.
It goes to +∞ for large positive x.

Answer 2

Answer:

$\lim_{x \to \infty} x^{5} = \infty$

$\lim_{x \to -\infty} x^{5} = -\infty$

Step-by-step explanation:

We have the following function:

$f(x) = (x^{2}+1)^{2}*(2x - 3)$

It is a fifth order polynomial. The end behavior of a function of x is the limit as x goes to infinity. So only the $x^{5}$ term is important.

So:

$\lim_{x \to \infty} x^{5} = \infty$

$\lim_{x \to -\infty} x^{5} = -\infty$