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Multiple Choice
Based ONLY on the maximum number of turning points, which of the following graphs could NOT be the graph of the given function? f(x)=x3+1
A
B
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.
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.
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.
The first graph has 2 turning points, the second graph has 1 turning point, and the third graph has 3 turning points.
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.