Suppose f is a polynomial function. If f (−2) = 7 and f (6) = −1, then the Intermediate Value Theorem guarantees which of the following? Justify your answer.

(a) f (0) = 0

(b) f (c) = 3 for at least one number c between − 2 and 6.

(c) f (c) = 0 for at least one number between − 1 and 7.

(d) − 1 ≤  f (x) ≤ 7 for all numbers in the closed interval [−2, 6].