APFIVE Identifying a Quadratic Model From Data
The table shows selected values for a function $$g$$.
| $$x$$ | -1 | 0 | 1 | 2 | 3 |
|---|---|---|---|---|---|
| $$g(x)$$ | -3 | -2 | 1 | 6 | 13 |
Which of the following statements is true about the function $$g$$?
A
$$g$$ is best modeled by a quadratic function, because the successive 2nd differences of the output values over equal-interval input values are constant.
B
$$g$$ is best modeled by a quadratic function, because the average rates of change over consecutive equal-length input-value intervals are constant.
C
$$g$$ is best modeled by a linear function, because the average rate of change over any length input-value interval is constant.
D
$$g$$ is best modeled by a linear function, because the successive 2nd differences of the output values over equal-interval input values are constant.
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