Problem
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
Solution
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 ：\(\boxed{\text{False}}\).
