Decide whether the following statement is true or false.
The average rate of change of $f(x)=3 x+9$ is 9 .

Choose the correct answer below.
True
False

Answer

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Answer

$\boxed{\text{False}}$.

Steps

Step 1 ：Define the function $f(x) = 3x + 9$.

Step 2 ：Calculate $f(1)$ and $f(0)$.

Step 3 ：Calculate the average rate of change over the interval $[0, 1]$ using the formula $\frac{f(b) - f(a)}{b - a}$.

Step 4 ：The average rate of change of $f(x)$ over the interval $[0, 1]$ is 3, not 9.

Step 5 ：Therefore, the statement 'The average rate of change of $f(x)=3 x+9$ is 9' is false.

Step 6 ：$\boxed{\text{False}}$.