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F-IF.9 Warmup M2-025-A05-V02

Compare function properties across representations, especially quadratic comparisons.

Compare constant linear rate with changing quadratic rate

Problem

Compare rate behavior for a linear table whose outputs increase by \(5\) each unit step and a quadratic table with first differences \(1,3,5,7\).

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Both tables have constant rates because each difference list follows a pattern.

Both rates change because both functions increase.

The linear outputs are 5,5,5 and the quadratic outputs are 1,3,5,7.

Linear first differences are 5,5,5. Quadratic first differences are 1,3,5,7 with second differences 2,2,2.

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Curriculum context

Course: Math II
Standard: F-IF.9
Category: Functions
Domain: Interpreting Functions
Objective: Compare function properties across representations, especially quadratic comparisons.
Problem type: Compare constant linear rate with changing quadratic rate