Problem

Use the displayed \(x-y\) table. Before comparing output changes, decide whether the consecutive input intervals are equal and justify the appropriate comparison method.

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What this problem is really about

Before comparing output changes, we need to know whether those changes occurred over equal input distances. We’ll temporarily ignore the output column and subtract consecutive input values. Equal gaps allow ordinary first differences to be compared directly; unequal gaps would require dividing each output change by its matching input change.

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The input intervals are equal because the x-values go up by 1 each time, so ordinary first differences can be compared.

The input intervals are not equal because the y-values change each row, so rates of change should be used instead of first differences.

The input intervals are not equal because the outputs are 2, 5, 8, and 11, so you should compare factors rather than first differences.

The input intervals are equal because the table goes from 0 to 3, so each interval is 3 and the changes can be compared.

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Use the displayed \(x-y\) table. Before comparing output changes, decide whether the consecutive input intervals are equal and justify the appropriate comparison method.

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