Which statement best describes the function below? \[ f(x)=x^{3}-x^{2}-9 x+9 \] A. It is a one-to-one function. B. It is not a function. C. It is a many-to-one function. D. It fails the vertical line test

Step 1 ：The given function is a cubic function. A cubic function is a function of the form \(f(x) = ax^3 + bx^2 + cx + d\), where a, b, c, and d are constants, and a ≠ 0. The graph of a cubic function is always a curve.

Step 2 ：A function is one-to-one if it passes the horizontal line test, which means that each y-value is paired with exactly one x-value.

Step 3 ：A function is many-to-one if it fails the horizontal line test, which means that some y-values are paired with more than one x-value.

Step 4 ：The vertical line test is used to determine whether a graph represents a function. If a vertical line intersects the graph in more than one point, then the graph does not represent a function.

Step 5 ：In this case, we need to plot the function to determine which statement is correct.

Step 6 ：From the graph, it is clear that the function passes the vertical line test, which means it is a function. However, it fails the horizontal line test, which means it is not a one-to-one function.

Step 7 ：Therefore, the function is a many-to-one function.

Step 8 ：Final Answer: \(\boxed{\text{C. It is a many-to-one function.}}\)