The differences between f(x) values are 3, 6, 9, 12. The differences between those are constant: 3. When "second differences" (for uniformly spaced x values) are constant, the function is quadratic.
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The degree of the function is equal to the level of differences that are constant. Linear (1st-degree) functions have 1st differences that are constant; cubic (3rd-degree) functions have 3rd differences that are constant.
If each level of differences increases in the same way, the function is exponential.
