The function y, equals, f, of, xy=f(x) is graphed below. Plot a line segment connecting the points on ff where x, equals, 0x=0 and x, equals, 1, .x=1. Use the line segment to determine the average rate of change of the function f, of, xf(x) on the interval 0, is less than or equal to, x, is less than or equal to, 1, .0≤x≤1.

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.

The function y = f(x) is graphed below. Plot a line segment connecting the points on f where x = 0 and x = 1. Use the line segment to determine the average rate of change of the function f(x) on the interval 0 ≤ x ≤ 1.

Learn how to find the average rate of change of a function f(x) on the interval 0 ≤ x ≤ 1. This problem demonstrates key concepts in calculus and algebra, using the secant line slope to calculate the average rate of change. Suitable for high school students in Grades 9-12.

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