Answer parts (a)-(e) for the function shown below.
\[
f(x)=x^{3}-2 x^{2}-x+2
\]
a. Use the leading coefficient test to determine the graph's end behavior. Which statement describes the behavior at the ends of $f(x)=x^{3}-2 x^{2}-x+2$ ?
A. The graph falls to the left and rises to the right.
B. The graph rises to the left and to the right.
C. The graph falls to the left and to the right.
D. The graph rises to the left and falls to the right.

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: \(\boxed{\text{A. The graph falls to the left and rises to the right.}}\)