decide whether the following statement is true or false. the average rate of change of ( f(x)=3x + 9 ) is 9…
decide whether the following statement is true or false. the average rate of change of ( f(x)=3x + 9 ) is 9. select the correct choice and, if necessary, fill in the answer box within your choice. a. false, the average rate of change is b. true
Answer
Explanation:
Step1: Recall the formula for average rate of change
The average rate of change of a function (y = f(x)) over an interval ([a,b]) is given by (\frac{f(b)-f(a)}{b - a}). For (f(x)=3x + 9), (f(b)=3b + 9) and (f(a)=3a + 9).
Step2: Calculate (\frac{f(b)-f(a)}{b - a})
[ \begin{align*} \frac{f(b)-f(a)}{b - a}&=\frac{(3b + 9)-(3a + 9)}{b - a}\ &=\frac{3b+9 - 3a - 9}{b - a}\ &=\frac{3(b - a)}{b - a}\ &=3 \end{align*} ]
Answer:
A. False, the average rate of change is (3)