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The given statement asks whether the average rate of change of \( f(x) = 3x + 9 \) is 9.

### Solution:
1. The formula for the average rate of change of a function \( f(x) \) over an interval \( [a, b] \) is:
   \[
   \text{Average rate of change} = \frac{f(b) - f(a)}{b - a}
   \]
   
2. However, the function \( f(x) = 3x + 9 \) is a linear function. For a linear function, the average rate of change between any two points is constant and is equal to the slope of the function.

3. In the function \( f(x) = 3x + 9 \), the slope is the coefficient of \( x \), which is 3. This means the rate of change of \( f(x) \) is always 3.

### Conclusion:
The statement that "The average rate of change of \( f(x) = 3x + 9 \) is 9" is **false**. The correct average rate of change is 3, not 9.

Would you like more details or clarifications on this? Here are some related questions:

1. How do you find the slope of a linear function from its equation?
2. Why is the average rate of change constant for a linear function?
3. How does the formula for the average rate of change differ for nonlinear functions?
4. Can the average rate of change ever equal the y-intercept of a linear function?
5. How does the average rate of change differ from instantaneous rate of change?

**Tip:** For any linear function, the slope is always the same as the average rate of change, no matter the interval.

The average rate of change of f(x) = 3x + 9 is 9.

Determine if the average rate of change of the linear function f(x) = 3x + 9 is 9. Learn about key concepts such as slope and the formula for average rate of change in linear functions. Suitable for high school students (Grades 9-11).

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