Question

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

Answer 1

`\lim_(x \to \infty) x^(5) = \infty`

`\lim_(x \to -\infty) x^(5) = -\infty`

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`

Answer 2

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.