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F-LE.1.a Warmup M1-028-A01-V01

Distinguish linear from exponential situations by equal differences versus equal factors over equal intervals.

Use first differences to identify a linear pattern

Problem

Calculate the first differences in the table. Are they constant? Use the differences to decide whether the pattern is linear.

Raw input/output table without computed differences, ratios, or classification cues. Open full size
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What this problem is really about

First differences measure how much the output changes from one row to the next. Because the input steps are equal, we’ll subtract each earlier output from the following output in a consistent direction. If those changes remain constant, they reveal a constant rate and provide the evidence needed to classify the pattern.

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Four variants of this problem type
Curriculum context
Course
Math I
Standard
F-LE.1.a
Category
Functions
Domain
Linear, Quadratic, and Exponential Models
Objective
Distinguish linear from exponential situations by equal differences versus equal factors over equal intervals.
Problem type
Use first differences to identify a linear pattern