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

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Answer 1 · 2018-02-23T22:54:38

See below.

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

$x^{3}$ $x^3$

as: $x \to \infty$ $x->oo$ $88888.888 x^{3} \to \infty$ $color(white)(88888.888)x^3->oo$

as: $x \to - \infty$ $x->-oo$ $888888 x^{3} \to - \infty$ $color(white)(888888)x^3->-oo$

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

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

How do you describe the end behavior for f(x)=x^3-3x^2+1f(x)=x3−3x2+1f(x)=x^3-3x^2+1?