Based ONLY on the maximum number of turning points, which of the following graphs could NOT be the graph of the given function? $f\left(x\right)=x^3+1$

• A.
• B.
• C.

Answer: (C)

Verified step by step guidance

1. Identify the degree of the polynomial function f(x) = x^3 + 1. The degree is 3, which is the highest power of x in the polynomial.
2. Recall that the maximum number of turning points of a polynomial function is one less than its degree. Therefore, for f(x) = x^3 + 1, the maximum number of turning points is 3 - 1 = 2.
3. Examine each graph to count the number of turning points. A turning point is where the graph changes direction from increasing to decreasing or vice versa.
4. The first graph has 2 turning points, the second graph has 1 turning point, and the third graph has 3 turning points.
5. Since the function f(x) = x^3 + 1 can have at most 2 turning points, the third graph, which has 3 turning points, could NOT be the graph of the given function.