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Given that the polynomial f(x) has 6 turning points, which of the following most accurately describes the degree of f(x)?

1) Linear
2) Quadratic
3) Cubic
4) Quartic

User Whisk
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1 Answer

4 votes

Final answer:

The most accurate description of the degree of f(x) is Quartic (4th degree) since it has 6 turning points.

Step-by-step explanation:

The polynomial f(x) with 6 turning points cannot be linear (1st degree) since it has multiple turning points and a linear function has at most 1 turning point (where the slope changes sign).

A quadratic function (2nd degree) has at most 2 turning points. Since f(x) has 6 turning points, it cannot be quadratic either.

A cubic function (3rd degree) has at most 3 turning points. Since f(x) has 6 turning points, it cannot be cubic either.

A quartic function (4th degree) has at most 4 turning points. Since f(x) has 6 turning points, the most accurate description of the degree of f(x) would be Quartic (4th degree).

User Pavlo Strokov
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