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. Understand the concept of turning points: A turning point is where the graph changes direction from increasing to decreasing or vice versa.
2. For a polynomial function of degree n, the maximum number of turning points is n - 1.
3. The given function is f(x) = x^3 + 1, which is a cubic polynomial. Therefore, it can have at most 2 turning points (3 - 1 = 2).
4. Analyze each graph: The first graph has 2 turning points, the second graph has 1 turning point, and the third graph has 3 turning points.
5. Identify the graph that does not fit: Since the function can have at most 2 turning points, the third graph with 3 turning points cannot be the graph of the given function.