What is the end behavior of y = 5 + 2x + 7x^2 - 5x^3?

May 30, 2017

As $x$ values get more negative, $y$ values get positive, and as the $x$ values get more positive, the $y$ values more negative.

Explanation:

The highest degree of this polynomial is $3$, so the traditional end behavior is the same as for $y = {x}^{3}$

graph{x^3[-2,2]}

That is, as $x$ gets more negative, the $y$-values get more negative and as the $x$-values get more positive, the $y$ values get more positive.

But notice that the sign of the 3rd degree term is negative in $- 5 {x}^{3}$, so the end behavior is the opposite. That is, as $x$ values get more negative, the $y$ values got positive, and as the $x$ values get more positive, the $y$ values more negative. The graph is given as follows:

graph{5+2x+7x^2-5x^3[-5,5,-20,30]}