Question

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

Answer 1

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 `-5x^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]}