https://file.aiquickdraw.com/mathbot/file/1727020366711dr31yfs7.jpg

To find the **average rate of change** of the function \( f(x) \) from \( x = 0 \) to \( x = 3 \), we need to use the formula:

\[
\text{Average rate of change} = \frac{f(3) - f(0)}{3 - 0}
\]

From the graph:
- \( f(0) = 5 \)
- \( f(3) = -1 \)

Now, applying these values to the formula:

\[
\text{Average rate of change} = \frac{-1 - 5}{3 - 0} = \frac{-6}{3} = -2
\]

So, the average rate of change from \( x = 0 \) to \( x = 3 \) is **-2**.

Would you like further clarification or additional details?

Here are 5 related questions to expand on this concept:
1. What does the negative average rate of change indicate about the function's behavior between \( x = 0 \) and \( x = 3 \)?
2. How would the average rate of change be affected if we calculated it from \( x = 3 \) to \( x = 6 \)?
3. What is the geometric interpretation of the average rate of change in terms of the graph?
4. How would the average rate of change differ from the instantaneous rate of change at a point?
5. Can the average rate of change be zero for a non-horizontal line?

**Tip:** The average rate of change is essentially the slope of the secant line connecting two points on the function's graph.

Use the graph of f(x) to evaluate the following: The average rate of change of f from x = 0 to x = 3. Give your answer as an integer or reduced fraction.

Learn how to calculate the average rate of change of a function f(x) from x = 0 to x = 3 using a graph. This problem involves key algebraic concepts such as functions and the rate of change formula. Suitable for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation