Which statement describes the function y = axn when a = 1 and n is odd?

The graph opens down.

The graph is symmetric about the origin.

The graph does not pass through the origin.

The graph has more than one x intercept

We have to choose the correct statement for the function y = a x^n, when a = 1 and n is odd. For example: y = x^3, or: y = x^5 etc. Those graphs pass through the origin and have just one x intercept (when y = 0, x = 0). It means that statements C and D are false. We know that f ( - x) = - x^n, so those functions are odd. And the graphs of odd functions are symmetric about the origin. Answer: B) The graph is symmetric about the origin.