Question

How do you describe the end behavior of `f(x)=x^5-4x^3+5x+2`?

Answer 1

See below.

Explanation:

For end behaviour of a polynomial we only need to be concerned with the degree and leading coefficient as we approach `oo` and `-oo`

For this example the degree is 5 and leading coefficient is 1.

as `x-> oo` , `x^5-> oo`

as `x-> -oo` , `x^5-> -oo`

(a negative value raised to an odd power is always negative )

So range of function is:

`[y in RR }`

Graph: graph{x^5-4x^3+5x+2 [-14.24, 14.24, -7.12, 7.13]}