Question

Use the average rate of change to describe the graph of f(x)
over the interval [0,2]
.

(1 point)
Responses

The average rate of change is 2.
The average rate of change is 2. - incorrect

The average rate of change is −2
.
The average rate of change is negative 2. - no response given

The average rate of change is −12
.
The average rate of change is negative 1 half. - no response given

The average rate of change is zero.

Answer 1

To find the average rate of change of a function \( f(x) \) over the interval \([0, 2]\), you can use the formula:

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

where \( a = 0 \) and \( b = 2 \).

1. **Evaluate \( f(0) \)**: Substitute \( x = 0 \) into the function \( f(x) \).
2. **Evaluate \( f(2) \)**: Substitute \( x = 2 \) into the function \( f(x) \).
3. **Plug the values into the formula**, using the results from steps 1 and 2.

Without knowing the specific function \( f(x) \), we cannot calculate the exact average rate of change.

However, based on your responses, you mentioned:
- The average rate of change could be 2, −2, −12, zero, or negative one half.

To say something meaningful without the specific function values:
- If \( f(2) > f(0) \), the average rate of change will be positive.
- If \( f(2) < f(0) \), the average rate of change will be negative.
- If \( f(2) = f(0) \), the average rate of change is zero.

If you have the specific function values for \( f(0) \) and \( f(2) \), please provide them, and I can help you calculate the average rate of change accurately. If no specific function is provided, please choose the response based on context given or additional insights into the values of the function at those points.