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.