Answer:
The second table
Step-by-step explanation:
When x-values are uniformly spaced (1 apart, for example), y-values are also uniformly spaced (have a common difference) when the function is linear.
The second table shows a common difference of 2 between y-values, so that function is linear.
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Table 1 differences are 2, 6, 10, so is likely quadratic.
Table 3 differences are -1, -3, -5, so is likely quadratic.
Table 4 differences are 1, 3, 5, so that one, too, is likely quadratic.
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Comment on differences
We call the differences between table values the "first differences." Then the differences between those are "second differences." Differences between the "n-1-th" differences are called the "n-th" differences. When n-th differences are constant (and not zero), the table values can be represented by a polynomial of n-th degree.
Hence when 1st differences are constant, the table represents a 1st-degree (linear) function. When 2nd differences are constant, the table represents a quadratic function.
