Problem preview

F-IF.9 Warmup M2-025-A05-V04

Compare function properties across representations, especially quadratic comparisons.

Compare constant linear rate with changing quadratic rate

Problem

Compare rate behavior for \(L(x)=-2x+7\) and a Q table with \(x=0,1,2,3\) and outputs \(5,5,7,11\).

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L has changing rate because its slope is negative.

L has constant rate −2. Q has first differences 0,2,4 and second differences 2, so Q’s rate changes.

Both functions have constant rates because Q’s differences follow a pattern.

L has constant rate 7 from its y-intercept.

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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