$y=−3x^3$ is one-to-one.
Work Step by Step
*Condition for One-to-one Function (the Horizontal Line Test): The graph of function $y=f(x)$ intersects each horizontal line at most once. Here from the graph of $y=−3x^3$, we can see that each horizontal line would intersect the graph only at most one time. In other words, for any value of x in the domain of $y=−3x^3$, there is only one corresponding value of y. Therefore, $y=−3x^3$ is one-to-one.