Step 1 :The leading coefficient test is a method used to determine the end behavior of a polynomial function. The end behavior of a function refers to the behavior of the graph of the function as x approaches positive infinity or negative infinity.
Step 2 :For the given function, the leading term is \(x^{3}\). The degree of the polynomial is 3, which is odd, and the leading coefficient is 1, which is positive.
Step 3 :According to the leading coefficient test, if the degree of the polynomial is odd and the leading coefficient is positive, the end behavior of the function is: the graph falls to the left and rises to the right.
Step 4 :So, the correct answer is A. The graph falls to the left and rises to the right.
Step 5 :Final Answer: \(\boxed{\text{A. The graph falls to the left and rises to the right.}}\)