Which of the following statements are true regarding the graph of the cubic polynomial f(x) = x3 + bx2 + cx + d?(Give reasons for your conclusions.)(a) It intersects the y-axis in one and only one point.(b) It intersects the x-axis in at most three points. (c) It intersects the x-axis at least once.(d) For I x I very large, it behaves like the graph of y = x3. (e) It is symmetric with respect to the origin.(f) It passes through the origin.
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Which of the following statements are true regarding the graph of the cubic polynomial f(x) = x3 + bx2 + cx + d?
(Give reasons for your conclusions.)
(a) It intersects the y-axis in one and only one point.
(b) It intersects the x-axis in at most three points.
(c) It intersects the x-axis at least once.
(d) For I x I very large, it behaves like the graph of y = x3.
(e) It is symmetric with respect to the origin.
(f) It passes through the origin.
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