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The problem is asking for the average rate of change of the function \( f(x) = 3x - 5 \) and its interpretation in terms of whether the function is increasing or decreasing.

1. **Average Rate of Change**: The average rate of change for a linear function \( f(x) = mx + b \) is simply the slope \( m \). In this case, the slope is \( 3 \).

2. **Interpretation**:
   - When the slope \( m > 0 \), the function is increasing.
   - When the slope \( m < 0 \), the function is decreasing.

For \( f(x) = 3x - 5 \), the slope is \( 3 \), which is positive, meaning the function is **increasing**.

Therefore, the correct answer is:
- **"The average rate of change is 3, and the function is increasing."**

The selection in the image is incorrect, as it says the function is decreasing.

Would you like more details on how we calculated the rate of change?

### 5 Related Questions:
1. What is the rate of change of the function \( f(x) = -2x + 4 \)?
2. How does the rate of change affect whether a function is increasing or decreasing?
3. Can the rate of change for a quadratic function be constant?
4. What is the average rate of change of \( f(x) = x^2 \) between \( x = 1 \) and \( x = 3 \)?
5. How can you interpret the slope of a linear function in real-world contexts?

### Tip:
For any linear function \( f(x) = mx + b \), the slope \( m \) always tells you the constant rate of change, making calculations very straightforward.

Determine and interpret the average rate of change for the function f(x) = 3x - 5.

This page explains how to determine the average rate of change for the linear function f(x) = 3x - 5. It includes details on identifying the slope and interpreting whether the function is increasing or decreasing. Suitable for students in Grades 9-12.

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