https://file.aiquickdraw.com/mathbot/file/17262404265814673u1cp.jpg

Let's analyze the graph and solve the questions based on it.

We have two questions:

### (a) Determine the net change between the indicated points on the graph.

The two indicated points on the graph are approximately:

- \( (1, 5) \)
- \( (4, 7) \)

The net change in the function \( f(x) \) between these two points is simply the difference in the \( y \)-coordinates:

\[
\text{Net change} = f(4) - f(1) = 7 - 5 = 2
\]

So, the **net change** is **2**.

---

### (b) Determine the average rate of change between the indicated points on the graph.

The average rate of change between two points on a graph is the slope of the secant line connecting those points. It can be calculated as:

\[
\text{Average rate of change} = \frac{f(4) - f(1)}{4 - 1} = \frac{7 - 5}{4 - 1} = \frac{2}{3}
\]

Thus, the **average rate of change** is **\(\frac{2}{3}\)** or approximately **0.67**.

---

Would you like further details or clarification?

Here are 5 related questions for further exploration:
1. What does the net change tell us about a function's behavior?
2. How would you calculate the instantaneous rate of change at a given point?
3. What is the significance of a positive or negative average rate of change?
4. How is the average rate of change related to the slope of a linear function?
5. How would you find the rate of change if the graph was curved at the points?

**Tip:** The average rate of change between two points can always be interpreted as the slope of a straight line connecting those points, even for nonlinear functions!

Determine the net change and the average rate of change between the indicated points on the graph.

Learn how to determine the net change and the average rate of change between two points on a graph. This problem involves calculating the difference in y-values and the slope of the secant line, suitable for students in Grades 10-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation