APFIVE The table gives values for a polynomial function $$g$$ at selected values of $$x$$:
| $$x$$ | 3 | 4 | 5 | 6 | 7 |
|---|---|---|---|---|---|
| $$g(x)$$ | -11 | -19 | -29 | -41 | -55 |
If $$a < b$$, then $$g(a) > g(b)$$ for all $$a$$ and $$b$$ in the interval $$3 < x < 7$$. Which of the following could be true about the graph of $$g$$ on the interval $$3 < x < 7$$?
The graph of $$g$$ is concave up because the function is decreasing, and the average rate of change over equal-length input-value intervals is decreasing.
The graph of $$g$$ is concave down because the function is decreasing, and the average rate of change over equal-length input-value intervals is decreasing.
The graph of $$g$$ is concave down because the function is decreasing, and the average rate of change over equal-length input-value intervals is increasing.
The graph of $$g$$ is concave up because the function is decreasing, and the average rate of change over equal-length input-value intervals is increasing.
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