Describe the graph of f(x) by selecting the correct statement about the average rat...

1. Calculate the average rate of change on interval [1, 3]: The average rate of change of a function $f(x)$ on an interval $[a, b]$ is given by the formula $\frac{f(b) - f(a)}{b - a}$. From the graph, we can identify the points $(1, 1)$ and $(3, 0)$. Therefore, the average rate of change on $[1, 3]$ is $\frac{0 - 1}{3 - 1} = \frac{-1}{2}$. Since the value is negative, the average rate of change is negative on this interval.
2. Calculate the average rate of change on interval [6, 7]: Using the same formula, we identify the points $(6, 2)$ and $(7, 0)$. The average rate of change on $[6, 7]$ is $\frac{0 - 2}{7 - 6} = \frac{-2}{1} = -2$. Since the value is negative, the average rate of change is negative on this interval.
3. Evaluate other intervals for comparison:
- Interval [0, 1]: Points are $(0, -1)$ and $(1, 1)$. Average rate of change = $\frac{1 - (-1)}{1 - 0} = \frac{2}{1} = 2$ (positive).
- Interval [3, 4]: Points are $(3, 0)$ and $(4, 1)$. Average rate of change = $\frac{1 - 0}{4 - 3} = \frac{1}{1} = 1$ (positive).
- Interval [0, 1] and [3, 4]: As calculated above, the average rate of change is positive on both these intervals.
4. Determine the correct statement: Based on the calculations, the average rate of change is negative on the interval [1, 3] and also on the interval [6, 7]. This matches the first option.