Math Problem Statement
Solution
To determine the least possible degree of the polynomial function from the graph, we can analyze the number of turning points.
Step-by-Step Solution:
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Count the Turning Points: A turning point is where the graph changes direction, either from increasing to decreasing or vice versa.
- From the image, we see five turning points.
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Determine Degree Using Turning Points: For a polynomial of degree , the maximum number of turning points it can have is . Therefore:
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Conclusion: The minimum degree of the polynomial is 6.
Would you like further details on how polynomial degree relates to turning points or have any questions?
Here are some related questions:
- How does the degree of a polynomial affect its end behavior?
- Can a polynomial of degree 6 have fewer than 5 turning points?
- What are the characteristics of polynomials with an odd degree?
- How do we determine the leading coefficient’s sign based on a graph?
- What would change if the polynomial had an additional turning point?
Tip: Remember, the degree of a polynomial function is at least one more than its maximum number of turning points.
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Math Problem Analysis
Mathematical Concepts
Polynomial Functions
Graph Analysis
Formulas
Degree of polynomial = Number of turning points + 1
Theorems
Turning Points and Polynomial Degree
Suitable Grade Level
Grades 10-12
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