Question

Calculate the average rate of change over the interval [−1,1]
using the given graph of the function.

(1 point)
The average rate of change is
.

Answer 1

To calculate the average rate of change of a function \( f(x) \) over the interval \([-1, 1]\), we use the formula:

\[
\text{Average Rate of Change} = \frac{f(b) - f(a)}{b - a}
\]

where \( a = -1 \) and \( b = 1 \).

To compute this, you need the values of the function at the endpoints of the interval, \( f(-1) \) and \( f(1) \). You can usually find these values by examining the function's graph at \( x = -1 \) and \( x = 1 \).

1. **Find \( f(-1) \)**: Locate the point on the graph corresponding to \( x = -1 \).
2. **Find \( f(1) \)**: Locate the point on the graph corresponding to \( x = 1 \).

Assuming we have those values, denote them as:
- \( f(-1) = y_1 \)
- \( f(1) = y_2 \)

Next, substitute these values into the average rate of change formula:

\[
\text{Average Rate of Change} = \frac{y_2 - y_1}{1 - (-1)} = \frac{y_2 - y_1}{2}
\]

Finally, replace \( y_1 \) and \( y_2 \) with their actual values from the graph to find the answer.

Since you haven't provided the graphical data or values, I cannot compute the precise average rate of change. Please refer to the graph to find the values of \( f(-1) \) and \( f(1) \), perform the calculation, and you will have your answer.