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To calculate the **average rate of change** of the function \( f(x) \) from \( x = -1 \) to \( x = 3 \), we can use the formula:

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

Where:
- \( a = -1 \) and \( b = 3 \),
- \( f(a) \) is the value of the function at \( x = -1 \),
- \( f(b) \) is the value of the function at \( x = 3 \).

### Step 1: Find \( f(-1) \)
From the graph:
- When \( x = -1 \), the corresponding value of \( f(x) \) appears to be \( f(-1) = 2 \).

### Step 2: Find \( f(3) \)
From the graph:
- When \( x = 3 \), the corresponding value of \( f(x) \) appears to be \( f(3) = 1 \).

### Step 3: Apply the formula
Now, substituting the values into the formula:

\[
\text{Average Rate of Change} = \frac{f(3) - f(-1)}{3 - (-1)} = \frac{1 - 2}{3 - (-1)} = \frac{-1}{4} = -\frac{1}{4}
\]

Thus, the average rate of change of \( f(x) \) from \( x = -1 \) to \( x = 3 \) is **\( -\frac{1}{4} \)**.

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Would you like further clarification or details on any of the steps? Here are five related questions to deepen your understanding:

1. How is the average rate of change related to the slope of a line?
2. What does a negative average rate of change indicate about the graph's behavior?
3. How do you interpret the rate of change in terms of real-world applications?
4. Can the average rate of change be calculated over different intervals on the same graph?
5. How would the answer change if we selected different points, like \( x = -2 \) to \( x = 1 \)?

**Tip:** The average rate of change between two points on a graph is the same as the slope of the secant line connecting those two points.

Find the average rate of change of f from x = -1 to x = 3. Give your answer as an integer or reduced fraction.

Learn how to calculate the average rate of change for the function f(x) from x = -1 to x = 3 using the formula for the slope of a secant line. This problem covers key concepts in algebra and is suitable for students in Grades 8-10.

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