Question

Use the given table to determine the appropriate model of the function. x       0             1             2             3             4       f(x)       3             6             12             21             33       linear exponential cubic quadratic

Answer 1

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.