Question

1. find the average rate of change over the interval -1,0.

Explanation:

Answer:

To find the average rate of change over the interval \([-1, 0]\), we use the formula for average rate of change: \(\frac{f(b) - f(a)}{b - a}\) where \(a = -1\) and \(b = 0\).

From the graph:

• At \(x = -1\) (point \(a\)), \(f(-1) = -1\) (the vertex of the parabola).
• At \(x = 0\) (point \(b\)), \(f(0) = 2\) (the \(y\)-intercept).

Substitute into the formula:
\[
\text{Average rate of change} = \frac{f(0) - f(-1)}{0 - (-1)} = \frac{2 - (-1)}{0 + 1} = \frac{3}{1} = 3
\]

(Note: The original problem’s options seem to have a typo or missing options, but based on the graph, the correct average rate of change is \(3\). If we assume a missing option with \(3\), that is the answer.)