Which statements correctly describe the graph of the function f of x is equal to x cubed minus 4 x squared minus 3 x plus 18 ? Choose three correct answers.

The function factors as f(x) = (x − 3)²(x + 2), so x = 3 is a double root and x = −2 is the other root. This makes C true and D false, since there are only two distinct solutions when y = 0. A cubic polynomial has domain and range equal to all real numbers, so B is true. Its derivative is 3x² − 8x − 3, which is positive, then negative, then positive, so the function increases, decreases, and increases again as described in E. Since the leading term is x³, as x approaches negative infinity, y approaches negative infinity, not positive infinity.

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