To solve this problem, we'll follow these steps:

Step 1: Understand the Average Rate of Change

The average rate of change of a function $f(x)$ over an interval $[a, b]$ is given by the formula:

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

In this case, the interval is from $x = 0$ to $x = 1$, so $a = 0$ and $b = 1$. Therefore, the average rate of change will be:

$\text{Average Rate of Change} = \frac{f(1) - f(0)}{1 - 0} = f(1) - f(0)$

Step 2: Locate Points on the Graph

You need to identify the points on the graph where $x = 0$ and $x = 1$.

• Find $f(0)$, which is the $y$-value of the function at $x = 0$.
• Find $f(1)$, which is the $y$-value of the function at $x = 1$.

Step 3: Draw the Line Segment

Once the points $(0, f(0))$ and $(1, f(1))$ are identified, you can draw a straight line segment connecting these two points on the graph. The slope of this line will represent the average rate of change of the function over the interval $[0, 1]$.

Step 4: Calculate the Average Rate of Change

Once you have identified the $y$-coordinates for $f(0)$ and $f(1)$, substitute them into the formula to calculate the average rate of change.

If you provide the graph, I can help you find the exact values for $f(0)$ and $f(1)$ and complete the calculation.

Let me know if you'd like to upload the graph, and feel free to ask any questions.

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Here are 5 related questions you might find helpful:

1. How do you interpret the average rate of change geometrically?
2. What is the difference between average rate of change and instantaneous rate of change?
3. Can the average rate of change be negative? What does that mean?
4. How do you calculate the average rate of change for non-linear functions?
5. What happens to the average rate of change if the interval becomes smaller?

Tip: The average rate of change of a function over an interval can also be thought of as the slope of the secant line connecting the two endpoints on the graph.