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M3-025-A09-V03
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F-IF.7.c
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M3-025-A09-V03
Graph polynomial functions using zeros, factorizations, and end behavior.
Estimate and classify polynomial turning points
Problem
A monotonic increasing cubic crosses the \(x\text{-}\text{axis}\) \(\text{once}\) and never reverses direction. State the turning-point count, describe the trend, and relate the count to the cubic degree bound.
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A
Count/order: 0 turns. Trend: increasing throughout with no reversal. Degree bound: a cubic may have anywhere from 0 to 2 turns.
B
Count/order: 1 turn, an unspecified maximum. Trend: increasing throughout despite the claimed reversal. Degree bound: a cubic may have up to 2 turns.
C
Count/order: 1 turn, an unspecified minimum. Trend: increasing→decreasing even though the graph never reverses. Degree bound: a cubic may have up to 2 turns.
D
Count/order: 2 turns, a maximum then minimum. Trend: increasing→decreasing→increasing. Degree bound: every cubic must have exactly 2 turns.
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Curriculum context
Standard F-IF.7.c
Category Functions
Domain Interpreting Functions
Objective Graph polynomial functions using zeros, factorizations, and end behavior.
Problem type Estimate and classify polynomial turning points
