Final answer:
The rate of change of the function y = 3x³ increases as x goes from -infinity to infinity because the derivative, 9x², is always positive for x other than zero.
Step-by-step explanation:
The function given is y = 3x³. To determine the rate of change as x goes from -infinity to infinity, we can examine the derivative of the function, since the derivative represents the rate of change of the function with respect to x. The derivative of y = 3x³ is dy/dx = 9x². Since 9x² is always positive for all x except at x = 0 where it is zero, the rate of change of the function is always positive. This means as x increases from -infinity to infinity, the function's rate of change also increases.
Therefore, the correct answer to the student's question is (a) Increases.