Question
The graph of a polynomial function has four turning points. What is the least possible degree of this polynomial?
(1 point)
Responses
3
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5
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6
(1 point)
Responses
3
3
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5
5
6
Answers
GPT-4o mini
The number of turning points of a polynomial function is related to its degree. Specifically, a polynomial of degree \( n \) can have at most \( n - 1 \) turning points.
In this case, since the polynomial has four turning points, the least possible degree \( n \) can be determined by the inequality:
\[ n - 1 \geq 4 \]
Solving this gives:
\[ n \geq 5 \]
Therefore, the least possible degree of the polynomial is 5.
So the answer is:
**5**
In this case, since the polynomial has four turning points, the least possible degree \( n \) can be determined by the inequality:
\[ n - 1 \geq 4 \]
Solving this gives:
\[ n \geq 5 \]
Therefore, the least possible degree of the polynomial is 5.
So the answer is:
**5**