Question

How do you describe the end behavior for `f(x)=x^3-3x^2+1`?

Answer 1

See below.

Explanation:

To find the end behaviour of a polynomial we only have to look at the leading coefficient and the degree. In this case:

`x^3`

as: `x->oo` `color(white)(88888.888)x^3->oo`

as: `x->-oo` `color(white)(888888)x^3->-oo`

The graph of `x^3-3x^2+1` confirms this:

graph{y=x^3-3x^2+1 [-14.24, 14.24, -7.11, 7.13]}