Use the table below to identify the consecutive-input interval with the greatest average rate of change.

Function table for comparing consecutive average rates, with rows 0 comma 9, 1 comma 6, 2 comma 4, and 3 comma 1.

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From x = 1 to x = 2, the average rate of change is greatest because y changes by -2 over 1 unit of x, so the rate is -2.

From x = 2 to x = 3, the average rate of change is greatest because the last interval drops from 4 to 1, so its rate is -3 and that is the biggest change.

From x = 0 to x = 3, the average rate of change is greatest because the total change is 1 - 9 over the whole table, so that interval should be used.

From x = 0 to x = 1, the average rate of change is greatest because y changes by -3 there, and 3 is larger than 2.

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Curriculum context

Course: Math I
Standard: F-IF.6
Category: Functions
Domain: Interpreting Functions
Objective: Calculate, estimate, and interpret average rate of change over an interval.
Problem type: Identify the interval with the greatest average rate of change from a table