Consider the polynomial function g(x)=10x^9-50x^6-500x^2 What is the end behavior of the graph of g?

It falls to the left and rises to the right.

Step-by-step explanation:

The polynomial function is given as;

g(x) =10x^(9) - 50x^(6) - 500x²

In this polynomial, the leading coefficient is 10. This is positive and also an even number and thus it means the graph will rise to the right.

Also, the degree of the polynomial is 9 since that's the highest degree of x. This degree is odd and it means the graph will point in the opposite direction to that of the leading coefficient. Thus, we can say it falls to the left.

So in summary, the end behavior of the graph of g is that it falls to the left and rises to the right.