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M1-029-A10-V04
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F-LE.1.b
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M1-029-A10-V04
Recognize constant rate of change as evidence for a linear model.
Diagnose a nonlinear table
Problem
Analyze the displayed table. Test linearity using interval slopes, identify any stronger pattern and exact model the data support, and state the limits of the evidence.
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A
slopes = -2,-3,-4 over equal intervals; verdict = not linear because slopes differ; stronger pattern = second differences -1,-1; family = exponential; model = y=6·0.5ˣ; scope = decreasing outputs prove exponential
B
slopes = -2,-3,-4 over equal intervals; verdict = not linear because slopes differ; stronger pattern = second differences -1,-1 are constant; family = quadratic; model = y=-(1/2)x²-(3/2)x+6; scope = table supports this quadratic model
C
slopes = -2,-3,-4 over equal intervals; verdict = linear because middle slope is -3; stronger pattern = second differences -1,-1; family = linear; model = y=-3x+6; scope = middle slope determines all intervals
D
slopes = -2,-3,-4 over equal intervals; verdict = not linear because slopes differ; stronger pattern = second differences -1,-1 are constant; family = neither; model = none; scope = no stronger pattern is available
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Curriculum context
Standard F-LE.1.b
Category Functions
Domain Linear, Quadratic, and Exponential Models
Objective Recognize constant rate of change as evidence for a linear model.
Problem type Diagnose a nonlinear table
