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

1 Answer
May 30, 2017

Answer:

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]}