Which graph has the same end behavior as the graph of f(x) = –3x3 – x2 + 1?

Given equation is f(x)=-3x^3-x^2+1

We have to identify the graph that has same end behaviour as of given equation.

It seems that you have missed to attach the given graph in question. So i will explain about how to find correct graph.

Given function has highest exponent 3 so that means degree = 3

which is an odd number.

We know that graph of odd degree polynomial always starts and ends in opposite direction.

Leading coefficient of given function is -3 which is negative.

We know that when leading coefficient is negative then graph starts from top.

Hence graph of given function will start from top and go to the bottom as shown in picture.

Now any given graph which opens from up and ends in bottom will be answer.

All polynomials having odd degree and negative leading coefficient will also have similar graph.