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

Feb 23, 2018

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: $x \to \infty$ $\textcolor{w h i t e}{88888.888} {x}^{3} \to \infty$

as: $x \to - \infty$ $\textcolor{w h i t e}{888888} {x}^{3} \to - \infty$

The graph of ${x}^{3} - 3 {x}^{2} + 1$ confirms this:

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